LIBRARY 
UNIVERSITY  OF  CALIFORNIA 

ST.   LOUIS  EXHIBIT 
NO 


LIBRARY 

OF  THE 


UNIVERSITY  OF  CALIFORNIA. 


GIF-r  OK 


u/-\ 


Accession 


Class 


J 


r 


EXPERIMENTAL    PHYSICS 


A  COURSE  FOR  FRESHMEN 


Being  a  Revision  of  Alexander's  Manual 


BY 

GEORGE    K.     BURGESS,     S.B, 

Docteur  de  /'  Universite  de  Paris 

Instructor  in  Physics,   University 

of  California 


BERKELEY,    CAL- 
1902 


Entered  According  to  Act  of  Congress  in  the  Year  1897,  by 

GEORGE  K.  BURGESS, 

In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


PREFACE. 

This  manual  represents  the  latest  step  in  the  development  of  a 
course  in  physics  for  Freshmen  at  the  University  of  California  under 
the  direction  of  Professor  Slate;  the  modifications  of  previous  texts 
are  not  radical,  but  reflect  the  present  instructor's  views  of  what  is 
suitable  for  the  freshman  class  at  this  time.  There  is  no  serious 
claim  to  originality,  either  in  subject  matter  or  in  method  of  pres- 
entation, both  of  which  are  largely  those  of  the  late  Professor 
Whiting,  and  of  Dr.  A.  C.  Alexander,  who,  until  recently,  gave  the 
instruction  in  this  course. 

The  course  has  been  modified  by  decreasing  the  time  of  instruc- 
tion in  the  laboratory  from  two  three-hour  periods  a  week  to  two 
periods  of  two  hours,  and  instead  of  one  lecture  there  are  now  two 
recitations  a  week.  By  this  change  it  is  hoped  that  the  students  will 
get  a  better  grasp  of  the  principles  involved  in  the  experiments. 

Among  the  main  points  by  which  this  manual .  differs  from  its 
predecessors  are  the  following: — 

Because  the  laboratory  period  has  been  reduced  from  three  to 
two  hours,  some  of  the  exercises  have  been  shortened. 

The  details  of  a  considerable  number  of  exercises  differ  from  those 
of  previous  texts,  and  many  of  the  experiments  have  been  entirely 
rewritten,  although  treating  in  general  of  the  same  principles  as 
heretofore,  v/ith  a  few  exceptions. 

More  emphasis  is  given  to  the  graphical  representation  of  results. 

Where  possible,  the  principle  of  an  experiment  is  summarized  in 
an  equation  by  the  student. 

Optional  experimental  parts  of  an  exercise  have  been  removed, 
due  to  the  shorter  laboratory  period,  and  also  because  in  practise 
this  has  been  found  by  the  author  to  be  of  questionable  benefit  in 
large  elementary  classes  for  which  the  ratio  of  the  number  of  students 
to  the  number  of  instructors  is  great. 

In  place  of  the  optional  portions  are  put  questions  or  problems 
that  the  student  may  solve  outside  of  the  laboratory,  if  he  finishes 
the  experimental  part  only  in  the  regular  period. 

Questions  are  occasionally  appended  to  an  exercise  that  require 
a  knowledge  of  principles  developed  in  the  class  room,  or  reference 
to  some  standard  descriptive  work. 

Finally,  the  exercises  have  been  arranged  in  four  groups  of  eleven 

(iii) 

102273 


IV  PREFACE. 

each,  the  exercises  of  each  group  being  so  written  that  the  student, 
with  the  aid  given  in  the  recitations,  may  intelligently  begin  with 
any  one.  Although  in  certain  instances  there  is  an  apparent  lack  of 
sequence,  yet,  on  the  whole,  this  system  seems  more  efficient  than 
the  one  previously  in  vogue,  in  which  the  students  were  started  by 
eights  in  succession,  when  in  a  section  of  eighty  students  some  were 
six  weeks  late  in  starting.  By  the  new  arrangement  two  weeks  are 
gained  in  every  eight,  when  all  the  students  may  devote  their  time  to 
back  work. 

The  author  is  indebted  to  the  members  of  the  Physical  Depart- 
ment for  helpful  advice,  and  especially  to  Mr.  C.  A.  Kraus,  who  has 
aided  in  many  ways  the  preparation  of  these  notes. 

GEORGE  K.   BURGESS. 

Berkeley,  July,   1902. 


CONTENTS. 

GENERAL    DIRECTIONS. 

GROUP     I. 

PROPERTIES    OF    FLUIDS. 

PAGE 

1.  Liquid  Pressure  and  Density .  10 

2.  Vapor  Pressure  and  Dalton's  Law 12 

3.  Variation  of  Vapor  Pressure  with  Temperature 15 

4.  Boyle's  Law  and  Voluminometer 17 

5.  Pressure  of  Gas  at  Constant  Volume 18 

HEAT. 

6.  Expansion  of  Gas  under  Constant  Pressure 19 

7.  Specific  Heat 20 

8.  Latent  Heat. 22 

9.  Mechanical  Equivalent  of  Heat 24 

SURFACE    TENSION. 

10.  Surface  Tension 25 

MECHANICS. 

11.  Principle  of  Moments 27 

GROUP    II. 

12.  Composition  of  Forces 29 

13.  Elasticity;  Laws  of  Stretching 31 

14.  Action  of  Gravity ...  32 

15.  The  Pendulum,  I    ... 34 

16.  The  Pendulum,  II  .   .   , 35 

SOUND. 

17.  Resonance  Tube 36 

18.  Velocity  of  Sound  in  Solids  .   .  .   .   .•   ;   .  *.   .*   .   .   .    .   .    .  38 

19.  Laws  of  a  Vibrating  String.    ........'.. 39 

(v) 


VI  CONTENTS. 

PAGE 

LIGHT. 

20.  Photometry 40 

21.  Refraction 41 

22.  Refraction  and  Dispersion 43 

GROUP    III. 

23.  Images  in  a  Spherical  Mirror 44 

24.  Convex  Lenses 47 

25.  Concave  Lenses 48 

26.  Drawing  Spectra 51 

MAGNETISM. 

27.  Laws  of  Magnetic  Action    .    .    . 52 

28.  Magnetic  Fields 54 

29.  Intensity  of  Earth's  Magnetic  Field,  1 56 

30.  Intensity  of  Earth's  Magnetic  Field,  II 57 

31.  Comparison  of  Magnetic  Fields 58 

ELECTRO-MAGNETIC    RELATIONS. 

32.  Electro-Magnetic  Relations 59 

33.  Laws  of  Electro-Magnetic  Action 62 

GROUP    IV. 

34.  Current  Determination 64 

ELECTRICITY. 

35.  Electrical  Resistance 65 

36.  Electromotive  Force.           67 

37.  Ohm's  Law 69 

38.  Divided  Circuits  and  Fall  of  Potential 70 

39.  Arrangement  of  Battery  Cells;  E.  M.  F.  and  Resistance  .   .  72 

40.  Comparison  of  Resistances  by  Wheatstone's  Bridge  ....  73 

41.  Heating  Effect  of  an  Electric  Current 74 

42.  Laws  of  Electrolysis 76 

ELECTRO-MAGNETIC    INDUCTION. 

43.  Electro-Magnetic  Induction 77 

44.  Earth  Inductor 79 


GENERAL    DIRECTIONS. 


BEGINNING  WORK. — The  class  will  be  divided  into  four  sec- 
tions, each  having  two  laboratory  periods  per  week  of  two  hours, 
preceded  by  a  recitation,  for  which  each  section  will  be  divided 
into  halves. 

The  laboratory  work  includes  forty-four  exercises,  divided  into 
sets  of  eleven.  As  soon  as  registered,  each  student  will  report 
at  the  laboratory  in  East  Hall  and  will  be  assigned  to  one  of  the 
first  eleven  experiments.  He  will  then  perform  in  succession  at 
the  following  exercises  the  cycle  of  eleven  experiments.  Exam- 
ple: A  student  assigned  to  the  yth  experiment  will  perform  the 
first  eleven  in  the  order  7,  8,  9,  10,  n,  i,  2,  3,  4,  5,  6.  Two 
weeks  will  be  allowed  at  the  close  of  this  cycle  for  the  correction 
and  completion  of  work.  A  new  set  of  experiments  will  then  be 
mounted,  and  it  will  then  be  impossible  to  reperform  any  of  the 
first  eleven  experiments  this  year. 

IN  THK  LABORATORY. — The  following  directions  are  necessi- 
tated largely  by  the  size  of  the  class. 

Students  will  work  in  pairs  and  may  choose  their  partners. 
Each  student  however  will  be  required  to  take  a  separate  set  of 
observations  for  each  experiment  and  to  write  up  his  notes  inde- 
pendently. All  data  must  be  recorded  at  the  time  of  observation 
in  the  note-book  and  not  on  scrap  paper. 

In  general,  at  least  three  independent  observations  of  each 
quantity  measured  are  to  be  taken  and  every  observation  recorded 
when  it  is  taken.  Notes  are  to  be  neatly  arranged  (see  sample 
note-book)  and  observations  recorded  so  as  to  be  distinct  from 
descriptive  or  other  written  matter,  and  when  practicable  results 
should  be  tabulated. 

Concise  but  clear  answers  are  wanted  to  questions  asked;  all 
inferences  should  be  in  the  words  of  the  student,  and  demonstra- 
tions should  be  complete.  Fractions  are  to  be  expressed  as 

decimals,  and  calculations  given  in  detail. 

(vii) 


8 


GENERAL   DIRECTIONS. 


For  the  heading  of  sheets,  name,  date,  etc.,  consult  sample 
note-book;  the  arrangement  there  indicated  must  be  exactly 
followed.  Separate  sheets  of  a  single  exercise  are  to  be  fastened 
securely  together;  turned  over  corners  will  not  be  accepted. 

PLOTTING. — In  several  exercises  the  results  are  to  be  expressed 
graphically  on  plotting  paper.  When  the  data  permits,  such 
scales  for  plotting  should  be  chosen  as  will  give  a  line  extending 
diagonally  across  the  paper.  Observed  points  on  the  curve 
should  be  indicated  by  crosses  and  not  by  dots  or  circles.  The 
known  quantity  is  to  be  plotted  horizontally  and  the  quantity  to 
be  studied,  vertically.  Plots  should  be  carefully  drawn  and 
properly  labeled.  In  general,  a  smooth  line  drawn  among  the 
points  corresponding  to  observations  best  represents  these  obser- 
vations. For  further  details  of  construction  of  a  plot,  see  sample 
note-book. 

PROBLEMS. — A  certain  number  of  problems  will  be  assigned 
during  the  year.  They  are  to  be  worked  on  laboratory  paper 
and  the  carbon  prints  are  to  be  handed  in. 

TRIGONOMETRICAL  RELATIONS. — For  those  students  who  are 
not    familiar    with   the  elements  of  trigonometry,  the  following 
definitions  will  suffice. 
A 


Consider  a  right-angled  triangle  ABC  of  sides  a,  b,  and  c. 
The  various  trigonometrical  functions  are  most  conveniently 
defined  in  terms  of  the  parts  of  such  a  triangle. 

The  sine  (written  sin)  of  an  angle  is  the  ratio  of  the  opposite 
side  to  the  hypothenuse. 

sin  A  =  ~  and  sin  G=£* 
b  b 


GENERAL   DIRECTIONS.  9 

The  cosine  (written  cos)  is  the  ratio  of  the  adjacent  side  to  the 
hypothenuse. 

.      c        ,          ~     a. 

cos  A  =  r  and  cos  C  =  .- 

b  b 

Evidently  also 

cos  A=sin  C  and  sin  Ar=cos  C. 
a=b  cos  C=b  sin  A,  c=b  cos  A=b  sin  C. 
The  tangent  (written  tan)  is  the  ratio  of  the  side  opposite  to 
the  side  adjacent. 

a  c. 

tan  A=-  and  tan  C—  - 
c  a 

Also  sin  A  sin  C. 

tan  A=  ---  -and  tan  C~ 


> 

cos  A  cos  C 

For  very  small  angles  the  sine  and  tangent  may  be  replaced 
by  the  angle  itself. 

UNFINISHED  WORK.  —  At  the  close  of  a  laboratory  period  the 
student  will  present  the  carbon  print  of  his  notes  to  the  instructor, 
-and  if  the  exercise  has  not  been  finished,  the  records  will  be 
stamped  with  the  date,  and  the  exercise  may  be  completed  later, 
but  is  to  be  handed  in  complete  within  two  weeks  after  the  date 
last  stamped  upon  it,  otherwise  it  must  be  repeated.  All  experi- 
mental data  taken  out  of  the  laboratory  must  be  stamped. 

In  general,  a  student  will  have  ample  time  to  complete  the 
experimental  part  of  any  exercise  in  a  laboratory  period;  but  if 
pressed  for  time,  calculations,  inferences,  demonstrations,  and 
answering  of  questions  may  be  performed  outside  of  the  labora- 
tory, as  above  indicated.  No  experiments  which  are  taken  home 
and  for  which  the  data  have  been  changed  will  be  accepted. 
Corrections  are  to  be  made  in  the  manner  indicated  in  the  sample 
note-book. 

GRADES.  —  The  following  system  of  marking  will  be  used:  — 

i  .   Excellence. 

2.  Satisfactory. 

3.  Deficient  in  inferences,  proofs,  or  answers  to  questions. 

4.  Repetition  of  part  of  experimental  work  required. 

5.  Repetition  of  whole  exercise  required. 


10  LIQUID   PRESSURE   AND   DENSITY.  [i 

Unsatisfactory  work  will  be  returned  for  correction.  All  defi- 
cient exercises  are  to  be  raised  to  grade  2,  otherwise  the  grade 
INCOMPLETE  will  be  given  for  the  term's  work. 

ORDER  AND  BREAKAGE. — Those  working  at  any  exercise  will 
be  held  responsible  for  the  apparatus  used  and  will  be  expected 
to  leave  it  in  good  order  when  through.  Breakages  should  be 
reported  to  the  instructor. 

GROUP    I. 

In  some  of  these  experiments  mercury  is  used.  Care  must  be 
taken  not  to  spill  it,  and  all  metals  should  be  kept  away  from  it. 
Refer  to  the  sample  note-book  for  suggestions  as  to  arrangement 
of  data  and  writing  of  notes.  In  general,  seek  to  finish  the 
experimental  work  in  the  time  allowed,  leaving  computations  and 
answers  to  questions  to  be  done  outside  of  the  laboratory  if 
pressed  for  time. 

i.     LIQUID    PRESSURE   AND   DENSITY. 

I.  Clamp  a  U-tube  in  a  vertical  position  to  a  burette  stand, 
with  the  bend  of  the  tube  resting  on  the  table.  Pour  into  this 
tube  enough  mercury  to  stand  about  5  cm.  above  the  table  in 
each  arm.  Then  pour  into  the  longer  arm  enough  water  to 
stand  about  13.6  cm.  above  the  end  of  the  mercury  column. 
Work  out  all  air  bubbles  with  a  fine  wire,  and  mop  up  any 
water  resting  on  the  mercury  in  the  short  arm  with  a  bit  of 
blotting-paper  tied  to  the  end  of  the  wire.  Measure  the 
heights  above  the  table  of  the  ends  of  the  mercury  and  water 
columns,  measuring  as  nearly  as  possible  to  the  center  of  the 
meniscus  in  each  case.  Are  the  liquids  in  the  two  branches 
at  the  same  level?  If  not,  why?  What  differences  are 
there  between  the  shapes  of  the  free  ends  of  the  two  columns? 
Account  for  these  differences. 


i]  LIQUID   PRESSURE   AND   DENSITY.  II 

Find  the  length  of  the  mercury  column  that  balances  the 
water  column,  and  also  the  ratio  of  the  two  balancing  columns 
(water  column  to  mercury  column). 

II.  Fill  the  longer  arm  of  the  U-tube  nearly  full  of  water, 
and  measure  the  length  of  the  water  column,    and   also  of  the 
mercury  column  that  balances  it.     Find  again  the  ratio  of  the 
balancing  columns.     Is  it  the  same  as  in  I?     This   ratio  will  be 
shown  to  be  equal  to  the  specific  gravity  of  mercury. 

III.  Fill  one  of  the  two  beakers,  or  jars,  with  water,  and  the 
other  with  a  saline  solution.       Place  a  leg  of  an  inverted  Y-tube 
in  each  of  the  liquids      Cautiously  draw  the  liquids  up  in  both 
legs  by  suction,  and  close  the  stem  of  the  Y  air  tight.      Why 
is  the  liquid  higher  in  either  branch  than  in   the  corresponding 
open   vessel?      Measure   the   height   of  each   column  of  liquid 
above  the  level  of  the  liquid  in  the  open  vessel.      Is  it  the  same 
for  both  liquids,  or  not?     Why? 

Does  it  make  any  difference  if  the  branches  of  the  Y-tube 
are  not  of  the  same  diameter,  or  are  not  held  vertically  ? 
Calculate  the  specific  gravity  of  the  saline  solution. 

IV.  Fill  the  two  branches  of  a  W-tube,  one  with  water  and 
the  other  with  wood-alcohol.       This   should   be  done   by  pour- 
ing  the   liquids    into   them   alternately,    a  small   quantity   at   a 
time.       Why    is    it    necessary    to   observe    this    precaution    in 
filling? 

Make  the  proper  measurements  and  calculate  the  specific 
gravity  of  the  wood-alcohol.  Draw  diagram  in  illustration. 

Why  is  it  unnecessary  to  have  the  ends  of  the  columns  at  the 
same  level? 

V.'  Answer  the  following  questions: — 

1.  To    what   class   of  liquids    is    the   method    of  the    U-tube 
inapplicable?     Why? 

2.  In  the  case  of  highly  volatile  liquids,  what    advantage  has 
the  method  of  the  W-tube  over  that  of  the  Y-tube  ? 

3.  Which  of  the  three  do  you  consider  to  be  the  most  general 
method? 


12  VAPOR    PRESSURE   AND    DALTON'S   LAW.  [2 

VI.  Distinguish  between  specific  gravity  and  density. 

If  pressure  is  defined  as  force  per  unit  area,  form  an  equation 
expressing  the  equality  of  pressures  of  the  two  liquids  in  the 
arms  of  the  U-tube  and  show  that  the  heights  are  inversely  as  the 
densities;  and  that  when  water  is  used  in  one  arm,  the  ratio  of 
the  heights  is  the  specific  gravity  of  the  other  liquid.  Show  that 
for  a  liquid,  pressure  is  proportional  to  depth. 

VII.  Calculate  the  total  outward  pressure  of  a  cube  of  mercury 
20  cm.  on  a  side.     What  is  the  weight  of  this  mercury? 


2.     VAPOR    PRESSURE   AND    DALTON'S    LAW. 

I.  Take  a  closed  tube,  at  least  80  cm.  long,  and  wipe  it  clean 
and  dry  with  a  swab  tied  to  a  long  and  stiff  wire.  Then  fill  it 
with  mercury  by  means  of  a  small  funnel.*  Close  the  open  end 
with  the  thumb  and  invert  the  tube  in  a  reservoir  of  mercury. 
After  removing  the  thumb,  does  the  mercury  in  the  tube  fall  to 
the  same  level  as  the  mercury  in  the  reservoir?  If  not,  why 
What  is  meant  by  the  barometric  pressure? 


*  Observe  the  following  directions  in  filling  the  tube  and  removing  air 
bubbles: — 

Fill  to  within  a  couple  of  cm.  of  the  open  end.  Close  with  the  thumb 
and  invert  a  number  of  times,  gathering  all  the  air  bubbles  adhering  to 
the  sides  into  one  large  bubble.  Then  hold  erect  and  fill  completely, 
pouring  the  mercury  in  slowly  and  working  out  all  air  bubbles  with  a 
fine  wire.  Again  invert  in  the  reservoir.  (The  amount  of  air  in  the  tube 
can  be  observed  by  tilting  it  until  the  closed  end  is  about  70  cm.  above 
the  table.)  To  further  remove  the  air,  place  the  thumb  tightly  ov.er  the 
open  end  of  the  tube  while  in  the  reservoir,  and  then  raise  and  carefully 
invert  it  a  number  of  times,  letting  the  partial  vacuum  pass  slowly  from 
one  end  of  the  tube  to  the  other,  and  finally,  holding  it  erect  with  the 
open  end  up,  take  the  thumb  off  and  fill  completely,  as  directed  above. 
This  operation  should  be  repeated  until  the  air  bubble  seen  when  the 
tube  is  tilted  has  been  reduced  to  the  smallest  possible  size.  The  height 
of  the  mercury  column  ought  now  to  agree,  writhin  one  cm.,  with  the 
barometric  reading  for  the  day.  If  it  does  not  so  agree,  repeat. 


2]  VAPOR    PRESSURE    AND    DAI/TON'S   LAW.  13 

Measure  the  height  of  the  mercury  in  the  tube  above  that  in 
the  reservoir.  Is  it  the  same  as  the  height  of  the  barometer?  If 
it  is  not,  explain  why. 

II.  Having    measured    the    height    of    the    mercury    column 
above  the  level  of  the  mercury  in  the  reservoir,  draw  as  much 
ether   as   possible    into   a    medicine    dropper,    and,   inserting   it 
into  the  reservoir  under   the  open   end  of  the  tube,  introduce  a 
few  drops  into  the  tube,  taking  great  care  not  to  introduce  any 
air.      Introduce   enough  so  that  some  of  the  liquid  will   remain 
unevaporated  on  top  of  the  mercury  column.      Describe  in  detail 
what  takes  place  when  the  ether  is  introduced.     Does  the  ether 
all  evaporate,  or  does  it  cease  to  evaporate  after  a  certain  amount 
has  been   introduced?     Explain  why.     When  is  a  vapor  said  to 
be  saturated  ? 

After  waiting  10  minutes  for  the  ether  vapor  to  come  to  the 
temperature  of  the  room,  measure  the  height  of  the  mercury 
column.  Why  is  it  less  than  before  the  introduction  of  the  ether? 
What  do  you  find  to  be  the  pressure  of  the  ether  vapor,  in  cm.  of 
mercury,  at  the  temperature  of  the  room  ?  (Record  this  tem- 
perature.) 

III.  («.)    Pour    more    mercury    into   the    reservoir,    leaving 
enough  space  for  the  mercury  in  the  tube  when  it  is  taken  out. 
With  the  tube  resting  on  the  bottom  of  the  reservoir,   measure 
again  the  height  of  the  mercury  column,   and  also  the  length  of 
the  tube  occupied  by  the  ether  vapor. 

(£.)  Raise  the  tube  so  that  its  lower  end  is  just  below  the  level 
of  the  mercury  inthe  reservoir  and  after  a  few  minutes  repeat 
the  measurements  of  (a). 

(V.)   Answer  the  following  questions: — 

1.  Was  the  pressure  of  the  ether  vapor  in  (a)  the  same  as 
in  (£)? 

2.  Was  its  volume  the  same  ? 

3.  The    temperature    being    kept   constant,    do    you    find   the 
pressure    of  saturated    ether    vapor    to    depend  on    its    volume, 
or  not? 


14  VAPOR     PRESSURE    AND    DALTON'S    LAW.  \2 

IV.  Remove  the  ether  from  the  mercury  by  wiping  its  surface 
with  a  piece  of  clean  blotting-paper  and  then  passing  it  through 
a  pinhole  at  the  point  of  a  paper  filter.      Pour  the  mercury  into  a 
I5o-cm.   bottle  with  a  rubber  stopper,  to  a  depth  of  2  or  3  cm. 
Be  sure  that  the  bottle  is  clean  and  dry  and  free  of  ether  vapor. 
(If  there  is  any  ether  vapor  in  the  bottle,  it  can  be  removed  by 
inserting  a  tube  and  blowing  it  out.)     Insert  the  short  arm  of  a 
U-tube,  at  least  50  cm.  long,  through  the  rubber  stopper.     See 
that  the  stopper  fits  closely  into  the  mouth  of  the  bottle  and  press 
it  in  as  tightly  as  possible.     Invert  the  bottle,  taking  care  not  to 
entrap  any  air  in  the  mercury  column.      Resting  the  bend  in  the 
tube  on  the  table,  measure  the  height  of  the  mercury  in  the  tube 
above,  or  below,  its  level  in  the  bottle.      Four  ether  into  the  tube 
so  as  to  stand  in  an   unbroken  column  15  or  20  cm.  deep,  and 
attach  a  rubber  bulb  to  the  open  end   of  the  tube.      By  pressing 
the  bulb,  force  a  little  of  the  ether  into  the  bottle,  taking  care  not 
to  force  in  any  air.     What  is  the  effect  of  introducing  the  ether? 

V.  Force  in  about  15  cm.  of  the  ether  in  the  tube  so  that  the 
ether  in  the  bottle  is  at  the  same  level  as  the  mercury  had  been 
before,  or  a  trifle  above  this  level.     The  volume  of  the  mixture  of 
air  and  ether  vapor  being  approximately  the  same  as  the  volume 
of    the  air   before  the  introduction  of  the  ether,  how  does  the 
pressure   within   the  bottle   compare  with  the  pressure  when  it 
contained  air   alone  ?     Did    the  evaporation    cease   immediately 
after  the  introduction  of  the  gasoline,  as  in   III?     If  it   did  not, 
explain  why.      What  do  you  find  to  be  the  effect  of  mixing  ether 
vapor  with  air,  the  volume  being  kept  constant  ? 

Watch  the  mercury  column  and  see  that  its  height  becomes 
constant  before  taking  the  measurements  in  VI.  The  mercury 
ought  to  become  stationary  in  15  minutes. 

VI.  Find  by  appropriate  measurements  the  increase  of  pressure 
within  the  bottle  over  the  pressure  before  the  introduction  of  the 
ether.     What  does    this  increase  of  pressure  represent?      How 
does  it  compare  with  the  pressure  of  ether  vapor  when  unmixed 
with  air  as  determined  in  II  ? 


3]  VAPOR   PRESSURE  AND  TEMPERATURE.  15 

Observe  and  record  the  temperature  of  the  room.  Is  it  the 
same  as  when  II  was  performed?  How  would  any  difference  in 
temperature  affect  the  pressure  of  the  ether  vapor? 

According  to  Dattori  s  law  the  pressure  of  any  vapor,  or  gas, 
in  a  gaseous  mixture*  is  the  same  as  it  would  be  if  it  occupied 
the  space  alone.  Do  the  results  obtained  in  VI  and  in  II  tend  to 
confirm  the  truth  of  this  law  ? 

VII.  Calculate  in  dynes  per  square  centimeter  the  barometric 
pressure,  also  the  pressure  of  the  ether  vapor  in  II,  in  the  same 
unit. 

Is  evaporation  a  cooling  or  a  warming  process?     Explain. 


3.  VARIATION  OF  VAPOR  PRESSURE  WITH 
TEMPERATURE. 

I.  Fill  a  deep  hydrometer  jar  with  water  at  about  55°.  When 
the  water  has  cooled  to  48°  (not  before)  set  in  the  jar  a  closed 
U-tube  with  a  few  cm.  of  ether,  free  of  air  bubbles,  f  in  the  closed 
end,  and  at  least  50  cm.  of  mercury  in  the  rest  of  the  tube. 
The  mercury  before  inserting  in  the  water  should  stand  a  few  cm. 
lower  in  the  open  arm  than  in  the  closed,  and  there  should  be 
enough  water  to  completely  cover  the  ether.  Describe  what  takes 
place  when  ether  is  warmed  in  this  way. 

Suspend  a  thermometer  in  the  jar  on  a  level  with  the  ether  and 
read  the  temperature  of  the  water.  J  At  the  same  time  measure 


*Dalton's  law  does  nut  apply  to  a  mixture  of  gases,  or  vapors,  that 
act  on  each  other  chemically,  or  to  a  mixture  of  vapors  from  liquids  that 
are  mutually  soluble. 

flf  there  is  any  air  above  the  ether,  ask  to  have  it  removed. 

JTo  read  a  thermometer  accurately,  the  observer's  eye  should  be 
placed  so  that  the  first  degree  mark  below  the  top  of  the  mercury  coin- 
cides with  its  reflection  in  the  mercury.  The  fraction  of  a  division 
above  this  mark  should  be  carefully  estimated  and  recorded  in  tenths  of 
a  degree. 


16  VAPOR   PRESSURE   AND   TEMPERATURE.  [3 

the  difference  in  level  between  the  mercury  in  the  two  arms  of  the 
U-tube.  Do  this  as  accurately  as  you  can  by  placing  a  metre  rod 
against  the  side  of  the  jar  and  sighting  across  the  top  of  each 
mercury  column.  It  will  injure  the  rod  to  put  it  into  the  water. 
Using  this  last  measurement  and  the  barometric  pressure  for  the 
day,  find  the  pressure,  in  cm.  of  mercury  and  in  dynes  per  square 
centimetre,  of  the  ether  vapor  within  the  closed  arm  of  the  tube. 
Stir  thoroughly  when  taking  readings. 

II.  If  necessary,  siphon  off  a  small  quantity  of  the  water  and 
replace  it  with  enough  cold  water  to  lower  the  temperature  about 
3  or  4  degrees,  not  more.      Repeat  the  measurements  of  the  last 
section. 

In  this  way  make  a  series  of  some  ten  observations  of  the  tem- 
perature and  pressure  of  the  ether  vapor,  cooling  it  down  to  the 
temperature  of  the  room  or  lower. 

III.  Plot  the  results  of  I  and  II  on  co-ordinate  paper  and  draw 
a  smooth  curve  to  show  the  relation  between  the  pressure  and 
temperature  of  ether  vapor. 

Do  you  find  the  pressure  of  the  ether  vapor  to  vary  uniformly 
with  the  temperature  or  not  ? 

IV.  Take  some  ether  in  a  small  test-tube  and  immerse  it  in 
water  at  about  30°,  adding  hot  water  gradually  until  the  ether 
begins  to  boil.     A  small,  clean  tack  or  other  sharp-pointed  object 
placed    in  the  ether  will  facilitate  boiling.      Record  the  tempera- 
ture of  the  ether  when  it  first  begins   to  bubble   as  the  boiling 
point. 

Find  from  the  plot  obtained  in  III  the  temperature  of  ether 
vapor  when  its  pressure  is  equal  to  the  barometric  reading  for 
the  day.  How  does  this  agree  with  the  boiling  point  of  ether 
just  found  ?  What  relation  may  one  infer  exists  between  the 
temperature  at  which  a  liquid  boils  and  that  at  which  the  pres- 
sure of  its  vapor  becomes  equal  to  the  atmospheric  pressure? 
Explain. 

V.  Write  not  less  than  one  hundred  words  on  the  properties  of 
saturated  vapors.      Explain  the  phenomenon  of  boiling. 


. 
4]  BOYLE'S  LAW  AND  VOLUMENOMETER.  17 


4.     BOYLE'S    LAW   AND   VOLUMENOMETER. 

I.  With  the  Boyle's  law  apparatus  take  a  set  of  five  readings 
of  pressure  and  of  corresponding  volumes,  covering  the  range  of 
the  apparatus.     To  the  difference  in  mercury  levels  what  quantity 
must  be  added  to  give  the  total  pressure  on  the  inclosed   gas? 
Assuming  the  tube  to  be  of  i  cm.  section,  plot  applied  pressures, 
i.  e.,  the  difference  in  mercury  levels,  in  terms  of  reciprocals  of 
volumes.      What  does  this  plot  show  to  be  the  relation  between 
the  pressure  and  volume  of  a  gas  when  the  temperature  is  con- 
stant?    Produce   the  line  drawn  until  it  cuts  the   pressure   axis 
and  compare  the  intercept  on  the  pressure  axis  with  the  barom- 
eter reading. 

II.  Unscrew  the  iron  cap  of  the  volumenometer  and  by  raising 
or  lowering  the  open  tube  adjust  the  level  of  the  mercury  in  the 
other  tube  to  some   point   between  the  middle   and    the   upper 
marks.     See  that  the  iron  cap  is  empty  and  replace  it,  screwing 
it  down  air-tight. 

Test  the  apparatus  to  see  that  it  is  air-tight.  (Describe  how 
you  do  this.) 

Notice  that  there  are  three  horizontal  marks  on  the  closed  tube 
and  that  the  mass  of  mercury  that  fills  this  tube  between  each 
pair  of  marks  is  recorded  on  the  apparatus,  so  that  the  volumes 
between  the  marks  may  be  calculated.  The  density  of  mercury 
is  13.6.  Find  the  volume  of  the  air  enclosed  above  the  middle 
mark  by  noting  the  change  in  volume  when  the  mercury  is  set  at 
the  upper  and  at  the  middle  marks  and  also  the  accompanying- 
change  in  pressure.  Two  equations  may  thus  be  formed,  one 
giving  the  difference  in  volumes  between  the  upper  and  lower 
marks  and  the  other  the  ratio  of  these  two  volumes  (in  terms  of 
the  ratio  of  the  pressures). 

Write  these  equations  and  find  volume  called  for. 

III.  Introduce  a  piece  of  iron  into  the  iron  cap  and  find  as  in 
II  the  volume  of  the  inclosed  air  to  the  middle  mark.      Calculate 


2 


1 8  PRESSURE   OF   GAS   AT   CONSTANT    VOLUME.  [5 

the  density  of  the  piece  of  iron,  after  finding  its  mass,  explaining 
the  process  you  use  and  writing  out  the  equations. 

IV.  Repeat  II  and  III,  using  the  middle  and  lower  marks, 
and  compare  results. 

5.  PRESSURE  OF  GAS  AT  CONSTANT  VOLUME. 

I.  Set  a  metre  rod  in  a  vertical  'position    alongside  the  open 
tube  of  a  simple  constant-volume  air  thermometer  with  a  fixed 
bulb.      Fill  the  space  about  and   above   the    bulb  with   water   at 
about  5°  or  10°,  and  stir  continuously.       Allow  ten   minutes  for 
the,  inclosed  air  to  come  to  the  temperature  of  the  bath,  and  then 
raise  or  lower  the  open  tube  so  as  to  bring  the  mercury  in  the 
stem  of  the  bulb  to  the  bottom  of  the  tube  through  which  the 
stem  is  thrust.      Read  on  the  metre  rod  the  heights  of  the  two 
mercury  columns,  and  take  the  temperature  of  the  bath,  stirring 
all  the  while. 

II.  Draw  off  some  of  the  water  and  replace  it  with  warmer 
water  so  as  to  raise  the  temperature  of  the    bath    about    10°.* 
After  waiting  ten  minutes,  repeat  the  operations    and    measure- 
ments of  I. 

In  this  way  make  a  series  of  observations  on  the  pressure  and 
temperature  of  the  inclosed  air,  raising  the  temperature  about  to0 
at  a  time, — and  carrying  it  as  high  as  can  be  conveniently  done 
with  boiling  water.  Arrange  the  results  in  tabular  form.  How 
did  the  pressure  of  the  inclosed  gas  (air)  alter  as  its  temperature 
increased?  Was  the  rate  of  change  uniform? 

III.  Calculate  the  average  increase  in  pressure  for  a  rise  of  one 
degree  in  temperature.      If  no  observation  was  made  at  o°,  calcu- 
late from  your  results,  using  the  atmospheric  pressure  for  the  day, 
the  pressure  that  the  gas  would  have  at  o°,  if  its  volume  was  kept 

*Do  not  try  to  obtain  a  rise  of  exactly  10°  in  temperature.  Better 
results  can  be  obtained  and  time  saved  if  the  bath  is  raised  a  trifle  over 
10°  and  then  stirred  till  the  inclosed  air  has  had  time  to  come  to  the 
same  temperature  as  the  surrounding  water,  whatever  that  may  be. 


6]          EXPANSION    OF   GAS    UNDKR    CONSTANT    PRKSSURK.  IQ 

constant.  Find  the  ratio  of  the  average  increase  in  pressure  per 
degree  to  the  pressure  at  o°. 

Calling  P0  the  pressure  at  o°,  Pt  the  pressure  at  /°,  and  a  the 
ratio  just  found,  write  the  equation  connecting  the  pressure  and 
temperature  of  a  gas  when  the  volume  is  constant. 

IV.  Plot  the  results  of  II,  plotting  the  temperatures  as  abscissae 
and  the  pressures  as  ordinates. 

Draw  the  straight  line  that  agrees  most  nearly  with  the  points 
located  on  the  plot.  Find  the  rise  of  this  line  (/.  e. ,  the  increase 
in  pressure  of  the  gas)  for  the  change  of  100°  in  temperature,  and 
also,  from  the  plot,  the  pressure  of  the  gas  at  o°.  From  these 
calculate  the  ratio  of  the  increase  in  pressure  per  degree  to  the 
pressure  at  o°.  How  does  this  agree  with  the  result  found  in 
III?  Why  should  this  last  be  the  more  reliable  of  the  two 
results? 

V '.  What  would  be  the  pressure  of  a  gas  at — 273°  C. ,  suppos- 
ing there  was  no  change  of  state  or  volume  ?  If  the  pressure 
of  a  gas  depends  on  the  motion  of  its  molecules,  would  the  mol- 
ecules have  any  motion  at — 273°  C.?  Then,  as  heat  is  the  energy 
due  to  molecular  motion,  according  to  this  reasoning  could  a  gas 
be  cooled  below — 273°  C.? 

This  temperature  is  called  absolute  zero.  The  temperature 
measured  in  Centigrade  degrees  from  absolute  zero  is  called  the 
absolute  temperature. 

6.     EXPANSION   OF   GAS    UNDER   CONSTANT 
PRESSURE. 

I.  Fill  the  space  about  the  closed  tube,  or  bulb,  of  the  air 
thermometer  with  ice-cold  water.  Set  the  slider  at  the  zero  of 
the  vertical  scale,  and  adjust  the  mercury  columns  so  that  the 
mercury  in  both  tubes  is  at  the  level  of  the  lower  end  of  the 
stuffing  box.  (The  mercury  column  can  be  set  quite  accurately 
by  sighting  across  the  end  of  the  brass  tube  surrounding  the 
glass. )  Read  the  volume  of  the  inclosed  gas  (air)  and  take  the 
temperature  of  the  water  bath,  stirring  thoroughly. 


20  SPECIFIC    HEAT.  [7 

II.  Raise  the    temperature  of  the  bath  as  in  Exercise  5,  II, 
about   10°  at  a  time,  and  repeat  for  each  temperature  the  opera- 
tions and  measurements  of  I,  waiting  ten  minutes  between  suc- 
cessive temperatures  to  allow  the  air  to  take  on  the  temperature 
of  the  bath.      What  was  the  pressure  of  the  inclosed  air  in  each 
case  ?     Was  it  the  same  ?     Was  the  expansion  of  the  air  uniform  ? 
Arrange  the  results  in  tabular  form. 

III.  Calculate  the  average  expansion  for  a  rise  of  one  degree  in 
temperature.      If  no  observation  was  made  at  o°,  calculate  from 
your  results  the  volume  that  the  gas  would  have  had  at  o°.     Find 
the  ratio  of  the  average  expansion  per  degree  to  the  volume  at 
o°, — in  other  words,  the  cubical  coefficient  of  expansion  between 
o°  and  i°. 

Calling  V0  the  volume  of  a  gas  at  temperature  o°,  Vt  the 
volume  at  t°,  and  a  the  coefficient  just  found,  write  the  law  of 
expansion  of  a  gas  at  constant  pressure  in  the  form  of  an  equation. 
This  is  called  the  law  of  Charles  or  Gay-Lussac. 

IV.  Plot  the  results  of  I  and  II  on  co-ordinate  paper,  plotting 
the  temperatures  as  abscissae  and  the  volumes  as  ordinates. 

Find  from  this  plot,  by  the  method  of  Exercise  5,  IV, 
the  expansion  for  a  change  in  temperature  of  100°  and  the 
volume  of  the  gas  at  o°.  Calculate  from  these  the  coefficient  of 
expansion  between  o°  and  i°.  Is  the  result  the  same  as  that 
obtained  in  III  ? 

V.  When  experiments  4,  5  and  6  have  been  performed,  hand  in 
a  paper  of  at  least  two  hundred  words  on  the  properties  of  gases. 

7.    SPECIFIC    HEAT. 

I.  Weigh  out  about  300  gr.  of  lead  shot  and  heat  it  in  a 
double  boiler.  After  the  water  begins  to  boil,  stir  the  shot  thor- 
oughly with  a  wooden  paddle,  continuing  until  the  temperature 
of  the  shot  becomes  constant. 

Have  ready  about  75  gm.  of  water  (weighed  to  0.5  gm.)  at  a 
temperature  of  5°  to  10°,  in  a  calorimeter  of  known  mass. 


7]  SPKCIFIC   HEAT.  21 

Note  carefully  the  temperature  of  the  shot  (stirring)  and  of  the 
water  (stirring),  and  as  quickly  as  possible  pour  the  shot  into  the 
water,  stirring  vigorously  all  the  while  and  note  the  rise  in  tem- 
perature of  the  water.  Read  the  temperature  of  the  mixture 
every  half  minute  for  five  minutes,  counting  from  the  instant  of 
mixing. 

From  the  results  obtained  calculate: — 

1.  The  number  of  heat  units  gained  by  the  water,  using  as 
heat  unit  the  calorie  or  the  heat  required  to  raise  the  temperature 
of  one  gramme  of  water  one  degree. 

2.  The  number  of  heat  units  lost  by  the  shot  (in  terms   of  s, 
the  specific  heat  of  lead)  or  the  ratio  of  the  heat  required  to  raise 
i  gm.  of  lead  one  degree  to  that  required  to  raise   i   gm.  water 
i°. 

Assuming  that  the  shot  and  water  are  alone  concerned  in  the 
transfer  of  heat,  what  relation  exists  between  the  heat  lost  and 
gained  by  the  shot  and  water  respectively  ?  Write  the  equation 
representing  this  relation  and  calculate  the  specific  heat  of  lead. 

II.  Calculate  from  this  result,  using  above  equation,  the  mass 
of  water  which  would  have  brought  the  mixture  to  a  temperature 
two  degrees  higher  than  that  of  the  room. 

Repeat  I,  using  this   mass  of  water  and  the  same  amount  of 
shot  as  before  and  other  conditions  also  the  same  as  in  I. 
Why  should  the  latter  result  be  the  better  ? 

III.  The  result  found  in  II  is  to  be  corrected  for  the  heat  lost 
to  cup,  assuming  the  specific  heat  of  the  cup  to  be  0.095;  a°d 
also  corrected  for  radiation  as  follows: — 

Construct  a  plot  with  times  as  abscissae  and  temperature  of 
water  and  mixture  as  ordinates;  project  the  line  (which  should 
be  straight  if  the  stirring  has  been  thorough),  representing  the 
temperatures  of  the  mixture,  back  until  it  cuts  the  ordinate  at  the 
instant  of  mixing.  This  ordinate  will  be  approximately  the  true 
temperature  of  the  mixture.  Why  ? 

Write  the  complete  equation  involving  all  of  the  above  quanti- 
ties and  recalculate  the  specific  heat  of  lead. 


22  LATENT    HEAT.  [8 

IV.  If  the  water  at  the  start  had  a  temperature  higher  than 
that  of  the  room,  would  the  value  of  s  found  have  been  high  or 
ow  ?  Explain. 

If  one  gramme  of  water  were  spilt  in  stirring,  what  would  be 
the  effect  on  the  value  of  s  ? 

8.    LATENT    HEAT. 

I.  Weigh    out    in  a  metal   cup,    which    has    been    previously 
weighed,  at  least  500  gm.  of  water  at  about  30°.     After  record- 
ing the  exact  temperature  of  the  water,  take  a  piece  of  ice  (about 
loo  gm.)   and  place  it   in   the    cup,  first  wiping  it  carefully  with 
damp  cotton.     Stir  the  mixture  thoroughly  and  take  its  tempera- 
ture  just  as  the  ice  disappears. 

Having  previously  weighed  the  water,  the  mass  of  the  dry  ice 
used  can  be  found  by  weighing  the  mixture  and  subtracting  the 
mass  of  the  water. 

II.  Calculate  in  order  the  following  quantities,  using  the  same 
unit  of  heat  as  in  Exercise  7 : — 

1.  The  heat  lost  by  the  water  surrounding  the  ice. 

2.  The    heat    lost  by  the  cup.      (In  calculating  this  quantity 
it  will  be  sufficiently  accurate  to  take  the  specific  heat  of  the  metal 
as  0.095.) 

3.  The   heat  required   to  raise  the  water  from  the  melted  ice 
from  o°  to  the  temperature  of  the  mixture. 

4.  The  total  heat  absorbed  by  the  ice  in  melting. 

5.  The  heat  absorbed  by  each  gramme  in  melting. 

The  latter  quantity  is  called  the  latent  heat  of  fusion  of 
water. 

III.  Fill   a  small  copper  boiler  about  two-thirds  full  of  water 
and  insert  through  the  cork  stopper  a  safety-tube  with  an  opening 
about  2  cm.  from  its  lower  end.      Connect  to  the  boiler  a  rubber 
tube  with   a  trap  for  collecting   the  water  condensed  in  the  tube 
and   a  delivery-tube  4   or  5   cm.  long.       Bring  the  water  in  the 
boiler  to  a  boil.     (If  at  any  time  steam  issues  vigorously  from  the 


8]  I.ATKNT  HKAT.  23 

safety-tube,  it  means  that  the  water  is  low  and  the  boiler  needs 
refilling.) 

Weigh  out  about  500  gm.  of  ice-water  in  a  metal  cup  of  known 
mass,  and  take  its  temperature.  Empty  the  water  out  of  the  trap 
and  hold  it  so  that  the  end  of  the  delivery-tube  is  immersed 
in  the  ice-water.  Stir  and  observe  the  temperature  as  it  rises. 
When  the  temperature  reaches  a  point  two-thirds  as  much  above 
the  temperature  of  the  room  as  the  original  temperature  of  the 
ice-water  was  below,  remove  the  delivery-tube.  Stir  and  take 
the  temperature  again  carefully.  Replace  the  cup  on  the  balance, 
and  find  the  increase  in  the  mass  of  the  water  due  to  the  steam 
that  has  been  condensed. 

IV.  If  the  temperature  of  the  water  was   two-thirds  as  much 
above  the  temperature  of  the  room  after  the  condensation  of  the 
steam  as  it  was  below  before  the  introduction   of  the  steam,  we 
may  safely  neglect  the  effect  of  the  air  and  surrounding  bodies,  for 
the  cup  will  lose  to  the  room,  by  radiation  and  conduction,  as 
much    heat   in   the  latter  part  of  the  experiment  as  it  gains  from 
it  in  the  first  part.     Using  the  same  unit  of  heat  and  the  same 
value  for  the  specific  heat  of  the  metal  cup  as  in  II,  calculate  in 
order  the  following  quantities:  — 

1.  The   total  amount   of  heat  imparted  to   the  water  and  the 
cup. 

2.  The  heat  given  out  by  the  water  from  the  condensed  steam 
in  cooling  from  100°  to  the  temperature  of  the  mixture. 

3.  The  total  amount  of  heat  given  out  by  the  steam  or  water 
vapor  in  changing  from  the  state  of  a  vapor  to  that  of  a  liquid. 

4.  The    heat   given  out  by  each  gramme   of  water  vapor  in 
changing  from  the  gaseous  to  the  liquid  state. 

The   latter  quantity  is    called   latent  heat  of  vaporization  of 
water. 

5.  Write  the  equations  representing  this  experiment. 

V.  Write  at  least  one  hundred  words  on  the  phenomena  of 
fusion  and  evaporation. 


24  MECHANICAL   EQUIVALENT   OF   HEAT.  [9 


9.  MECHANICAL  EQUIVALENT  OF  HEAT. 

I.  Take  two  bottles  and  put  in  each  of  them  a  kilogramme  of 
lead  shot.     Place  these  bottles  in  a  mixture  of  ice  and  water. 

When  the  shot  in  one  of  the  bottles  has  cooled  about  3°  below 
the  temperature  of  the  room,  shake  it  thoroughly,  and  pour  it 
into  the  tube  provided,  about  one  metre  long,  and  close  the  end 
of  the  tube  securely  after  taking  the  temperature  of  the  shot  by 
inserting  a  thermometer.  Raise  the  end  of  the  tube  containing 
the  shot  with  sufficient  velocity  to  keep  the  shot  from  falling,  and 
when  it  reaches  a  vertical  position,  let  the  shot  fall  vertically,  like 
a  solid  mass,  through  the  length  of  the  tube.  Repeat  this  again 
and  again,  keeping  count  of  the  number  of  times  the  shot  falls.* 

After  the  shot  has  fallen  through  the  length  of  the  tube  a 
hundred  times,  insert  a  thermometer  through  a  side  opening,  and 
take  its  temperature  again.  Why  has  the  temperature  of  the 
shot  risen  above  that  of  the  room  ? 

II.  Replace  the  shot  in  the  ice- water  to  cool,  and  while  the 
tube  is  still  warm,  repeat  the  operations  and  measurements  of  I, 
using  the  shot  from  the  other  bottle,  which  should  be  about  3° 
below  the  temperature  of  the    room.      (Its  temperature   can  be 
raised   by    shaking   the    bottle,    if  it   is    too  low.)     Repeat   the 
experiment  in   this  way,  cooling  one  bottle  of  shot  while   using 


*  PRECAUTIONS,  ETC. — The  shot  should  not  be  raised  too  suddenly,  so 
as  to  throw  it  violently  against  the  side  of  the  tube,  nor  should  the  tube 
be  raised  or  lowered  so  as  to  lengthen  or  shorten  the  distance  fallen 
through  by  the  shot. 

It  is  well,  also,  to  hold  the  tube  about  a  foot  from  each  end,  so  that 
there  is  no  danger  of  any  heat  being  imparted  to  the  shot  from  .  the 
hands.  The  following  method  of  raising  the  shot  and  reversing  the  tube 
is  recommended:  Lay  the  tube  on  the  table,  and  raise  the  end  contain- 
ing the  shot,  while  the  other  end  rests  on  the  table.  Let  the  shot  fall, 
and  then  lower  the  raised  end.  Raise  the  other  end,  which  now  con- 
tains the  shot,  and  let  the  shot  fall  again.  Then  lower  this  end,  and 
again  raise  the  end  which  contains  the  shot;  and  so  on. 


ID]  SURFACE   TENSION.  25 

the  other,   making  five   determinations   and   using   the   average 
result  in  what  follows. 

III.  Remove  the  stopper  and  measure  the  distance  from  the 
inner  end  of  the  stopper  to  the  top  of  the  shot.       What  is  the 
average  distance  fallen  through  by  the  shot  in  each  reversal  of 
the  tube?     Explain.      In  one  hundred  reversals?     How  far  would 
the  shot  have  to  fall  to  raise  its  temperature  one  degree?     How 
for  would  one  gramme  have  to  fall  to  raise  its  temperature  the 
same  amount  (one  degree)  ?      How  much  work,  in  ergs,  would 
be  required  to  raise  one  gramme  of  shot  one  degree  in  tempera- 
ture?    The  specific  heat  of  lead  is  about  0.032.       Using   this, 
calculate,  in  the  ergs,  the  amount  of  work  necessary  to  raise  one 
gramme  of  water  one  degree  in  temperature.     This  last  quantity 
is  called  the  mechanical  equivalent  of  the  heat  unit. 

IV.  Write  the  equation  representing  this  exercise. 
What  are  the  chief  sources  of  error  in  the  experiment? 

V.  Power  is  the  rate  of  doing  work,  and  may  be  measured  in 
ergs    per   second,   or    in  watts,   which    is    io7  ergs    per   second. 
io7  ergs  is  a  joule.       Calculate  the  work  done  in  joules  by  the 
shot  falling  100  times  the  length  of  the  tube,  and  if  this  operation 
akes  3  minutes,  calculate  the  power  developed  in  watts. 

io.     SURFACE  TENSION. 

It  is  of  capital  importance  that  the  rectangles  and  beakers  used 
in  this  exercise  be  clean.  They  should  be  thoroughly  washed  in 
hot  water  before  being  used  and  for  every  change  from  one  liquid 
to  another. 

The  Jolly  balance  should  be  read  by  bringing  a  definite  point, 
as  the  lower  end  of  the  spring,  in  a  horizontal  line  with  its  image 
in  the  mirror.  The  reading  is  facilitated  by  bringing  a  card 
pierced  with  a  small  hole  (3  mm.  in  diam.)  close  before  the  eye 
and  standing  in  front  of  the  scale  at  such  a  distance  that  the 
object  and  image  are  seen  sharply  focused  at  the  same  time. 

I.  Fill  a  beaker,  about  7  cm.   in  diameter,   with  a  solution  of 


26  SURFACE    TENSION.  [lO 

soap  in  water.  Replace  the  pans  of  a  Jolly  balance  by  a  wire 
rectangle  2  cm.  wide,  hung  vertically,  and  hold  the  beaker  so 
that  the  rectangle  is  immersed  to  a  certain  definite  depth  in  the 
soap  solution.  See  that  there  is  no  soap  film  within  the  rectangle, 
and  read  the  balance. 

Let  the  rectangle  dip  in  the  soap  solution  so  that  a  film  is 
formed  within  it.  Raise  or  lower  the  beaker  so  that  the  rect- 
angle is  immersed  to  the  same  depth  as  before  and  again  read 
the  balance.  What  difference  does  the  presence  of  the  film  make 
in  the  reading  of  the  balance  ?  To  what  force  is  the  elongation  of 
the  spring  due? 

Take  four  independent  sets  of  readings. 

II.  Repeat  the  measurements  of  I,   using  rectangles  about  4 
and  6  cm.   wide.     How  do  you  find  the  tension   of  the  film  to 
vary  with  its  width  ? 

III.  Find  the  elongation  of  the  spring  produced    by  a  small 
known    weight, — some  fraction  of  a   gramme.      How    does    the 
elongation  vary  with  the  force  producing  it?     Test  this. 

Calculate  the  tension  in  dynes  (980  dynes=weight  of  one 
gramme)  of  each  of  the  three  films  in  I  and  II.  As  a  film  has 
two  surfaces,  the  width  of  the  surface  in  apparent  tension, 
neglecting  that  about  the  wires,  will  be  equal  to  twice  the  width 
of  the  rectangle.  Using  this,  calculate  in  dynes  the  average 
tension  of  the  soap  solution  across  each  cm.  of  the  surface. 

The  tension  across  a  unit  length  of  the  surface  of  a  liquid  is 
called  the  surface  tension  of  that  liquid. 

IV.  Clean  the  beaker  and  rectangle    thoroughly,   and    repeat 
the  measurements  of  II  with  water  fresh  from  the  faucet. 

As  a  film  can  not  be  formed  with  pure  water,  take  the  reading 
of  the  balance  when  the  upper  side  of  the  rectangle  is  just  above 
the  surface  of  the  water  and  again  when  it  breaks  away  from  this 
surface.  The  force  measured  in  this  way  may  be  regarded  as  due 
entirely  to  surface  tension,  although  this  is  not  strictly  true. 
Take  four  sets  of  readings. 

Calculate  the  surface  tension  of  the  water.  How  does  it  com- 
pare with  that  of  the  soap  solution? 


Il]  PRINCIPLE   OF    MOMENTS.  2J 

V.  Using  the  same  rectangle,  find  the  surface  tension  of  hot 
water  from  the  heater  at  the  sink.      Does  the  temperature  affect 
the  surface  tension  appreciably,  and  how  ? 

VI.  If  the  rectangle  4  cm.  wide  carries  a  soap  film  2  cm.   high, 
what  is  the  work  done  in  forming  this  film?     What  is  the  energy 
per  square  centimeter  of  this  film  ?       How    does   this    quantity 
compare  with  the  surface  tension? 

ii.    PRINCIPLE   OF    MOMENTS. 

I.  (#.)  Attach  a  light  metal  frame  to  the  table  so  that  it  can 
rotate  freely  about  a  pivot.  '  Fasten  two  spring  balances  to  the 
frame  with  twine,  at  equal  distances  on  opposite  sides  ol  the 
center,  and  draw  them  out  so  that  they  are  parallel.  Read  the 
balances.  Does  a  force  produce  the  same  effect  if  transferred 
along  its  line  of  action  ?  How  test  this? 

Pull  one  of  the  balances  out  until  the  tension  is  doubled, 
keeping  them  still  parallel.  What  does  the  other  balance  regis- 
ter? When  a  force  tends  to  produce  rotation  about  a  pivot, 
what  is  the  effect  of  doubling  this  force  upon  the  force  opposing 
the  rotation  ? 

(<5.)  Move  one  of  the  balances  to  a  point  twice  the  distance 
from  the  center  as  in  (a)  and  pull  it  (parallel  to  the  other  balance) 
until  it  registers  the  same  tension  as  before.  Read  both  balances. 

The  perpendicular  distance  from  the  center  of  rotation  to 
the  line  of  action  of  a  force  is  called  its  lever  arm.  When  a 
force  tends  to  produce  rotation  about  a  point,  what  do  you  find 
to  be  the  effect  of  doubling  the  lever  arm  upon  the  force  oppos- 
ing the  rotation  ? 

(V.)  The  tendency  of  a  force  to  produce  rotation  about  a  point, 
according  to  (a)  and  (^),  is  proportional  to.  the  product  of  what 
two  quantities  ?  This  product  is  called  the  moment  of  the  force 
about  the  point  considered,  and  is  usually  taken  positive  in  sign 
when  the  force  tends  to  produce  rotation  in  a  counter-clockwise 
direction,  and  negative  when  it  tends  to  produce  rotation  in  the 
opposite  direction. 


28  PRINCIPLE    OF    MOMENTS.  [ll 

II.  (a.)  Take  a  beam  suspended  so  as  not  to  rub  the  surface  of 
the  table,  and  connect  its  middle  point  to  a  nail  in  the  table  by 
means  of  a  spring  balance.      Attach  two  balances  to  two  screw- 
eyes,    one    metre    apart,  on    the    opposite    side  of  the  beam    at 
unequal    distances    from  its  middle  point  and  to    corresponding 
nails  in  the  table.     Tighten  the  cord  attached  to  the  first  balance. 
Read  all  three  balances,  and  measure  the  distances  between  their 
points  of  attachment  to  the  beam. 

(<£.)  Loosen,  or  tighten,  the  cords  a  little  and  read  the  balances 
again. 

(V.)  Calculate  the  moment  of  each  of  the  forces  in  (a)  about 
some  point  of  the  beam.  Give  these  moments  their  proper 
signs,  and  find  their  algebraic  sum.  Do  the  same  for  the 
forces  in  (6).  What  is  your  conclusion  as  to  the  value  of 
the  sum  of  their  moments  when  a  number  of  parallel  forces  in 
the  same  plane  act  on  a  rigid  body  so  that  it  is  held  in 
equilibrium  ? 

III.  Attach  three  balances  at  random  to  the  frame  used  in   I, 
and    to  nails    in    the    table.      Tighten    the    cords   and    read    the 
balances.      Draw,  on  a  sheet  of  paper  laid  underneath  the  frame, 
a  line  parallel  to  the  line  of  action  of  each  of  the  forces  measured 
by  the  balances.      Remove  the  frame  and  measure  carefully  the 
lever  arm  of  each  force  about  the  pivot  as  a  center.      Calculate 
the  moments  of  the  forces  about  the  pivot  and  find  their  algebraic 
sum.      In  addition  to  finding  the  sum  of  the  moments  about  the 
pivot,  find  also  the  sum  of  the  moments  of  the  forces  about  some 
point  outside  the  pivot.      Do  you  find  the  sum  of  the  moments  to 
be  approximately  the  same  wherever  the  center  of  moments   is 
taken,  or  not?     Explain. 

IV.  Repeat  III,  removing  the  pivot,  so  that  the  frame  is  free  to 
move    in  any  horizontal  direction.     Make  the  proper  measure- 
ments and  calculate  the  sum  of  the  moments  of  the  forces  about 
some  point  on  the  table  taken  at  random.     Do  the  same  for  some 
other  point  on  the  table.     Do  you  find  the  sum  of  the  moments 
to  be  approximately  the  same  wherever  the  center  of  moments  is 
taken  ? 


12 


:]  COMPOSITION   OF    FORCES.  2Q 


V.  If  any  number  of  forces  in  the  same  plane  act  upon  a  rigid 
body  so  that  it  is  held  in  equilibrium,  what  do  you  conclude  from 
the  results  of  this  exercise  must   be  the  algebraic  sum  of  their 
moments  about  any  point  in  that  plane?     The  correct  answer  to 
this  question  is  called  the  principle  of  moments. 

VI.  Two  equal,  parallel  forces  in  opposite  directions  constitute 
a  couple.     The  perpendicular  distance  between  them  is  called  the 
arm  of  the  couple. 

Let  a  be  the  arm,  and  F  one  of  the  component  forces  of  a 
couple.  Find  the  moment  of  this  couple  about  any  point.  Is  it 
the  same  for  all  points  ?  Demonstrate  this  for  any  point  within 
and  one  without  the  lines  of  action  of  the  forces. 

GROUP   II. 

In  general,  students  will  begin  with  the  exercise  corresponding 
to  that  they  began  with  in  Group  I.  Thus  he  who  started  with 
the  5th  exercise  will  now  take  the  i6th,  and  so  on. 

12.    COMPOSITION    OF    FORCES. 

I.  Take  a  stout  beam,  over  a  metre  long,  and  find  its  weight 
(in  Ibs. )  by  means  of  a  spring  balance. 

Attach  cords  of  equal  length  to  screw-eyes  near  the  ends  of  the 
beam,  and  suspend  it  by  these  cords  from  two  3O-lb.  spring 
balances  hung  from  nails  in  the  wall,  at  the  same  distance  apart 
as  the  screw-eyes  in  the  beam.  Read  the  balances.  What 
relation  exists  between  the  combined  readings  of  the  balances 
and  the  weight  of  the  beam  ? 

II.  Suspend  a  mass  of  metal,  weighing  over  30  Ibs.,  from  the 
middle    of  the   beam    and    read  the   balances   again.       Do    the 
balances  read  alike  ?     Why?     How  can    you  find  the  weight  of 
the    metal    from    the  readings    of  the    balances?     What    is   the 
weight  as  thus  found? 


30  COMPOSITION    OF    FORCES.  [l2 

III.  Hang  the  mass  of  metal  from  a  point  to  one  side  of  the 
middle  of  the  beam  and  read  the  balances  again.      Why  do  they 
not  read  alike  now  ?     Does  the  relation  found  in  I  between  the 
total  suspended  weight  and  the  combined  readings  of  the  balances 
still  hold  true  ?     Measure  the  horizontal  distances  from  the  cord 
by  which  the  weight  is  hung  to  the  cords  to   which  the  balances 
are  attached.      How  do  the  products  formed  by  multiplying  each 
distance  by  the  reading  of  the  corresponding    balance  (less  one- 
half  the  weight  of  the  beam)  compare? 

In  general,  what  is  the  resultant  of  two  parallel  forces  in  the 
same  direction  equal  to:  what  is  its  direction:  and  how  is  its  line 
of  action  situated  with  reference  to  the  component  forces? 

IV.  Hang  two  3o-lb.  spring  balances  from  two  nails  above  the 
blackboard,  at  least  one  metre  apart,  and  connect  the  balances  by 
a  cord  somewhat  over  a  metre  long.     From  the  middle  point  of 
this  cord  suspend  the  mass  of  metal  used  in  II  and  III.      Draw 
on  the  blackboard  lines  parallel  to  the  two  parts  of  the  cord  and 
lay  ,orT  on  these  lines,  from  their  intersection,  length?  proportional 
to  the  tension  in  each  part  of  the  cord  as  registered  by  the  proper 
balance.     Construct  a  parallelogram  with  these  lines  as  sides  and 
draw  the  vertical  diagonal.      Measure  the  length  of  this  diagonal 
in  Ibs.,   using  the  same  scale  as  was  used  for  the  sides  of  the 
parallelogram.      How    does    this    diagonal    compare   in  direction 
and  length  with  the  downward  force  (weight)  of  the  mass  sus- 
pended from  the  cord?     What  is  the  value  of  the  weight  as  found 
by  this  method  ? 

V.  Hang  the  mass  of  metal  to  one  side  of  the  middle  of  the 
cord,  and  construct  another  similar  parallelogram  of  forces.      Is 
the  relation  between  the  diagonal  and  the  weight  of  the  suspended 
mass  the  same  as  in  IV?     What  is  the  value  of  the   weight  as 
found  from  this  parallelogram? 

VI.  Hang  the  mass  of  metal  by  a  single  cord  from  one  of  the 
nails.      Attach  a  spring  balance  to  the  cord,  near  the  bottom  of 
the  blackboard,  and  pull  it  horizontally  one  foot  from  the  vertical. 
Note  the  reading  of  the  balance,  and  measure  the  vertical  distance 
from  the  nail  to  the  line  of  action  of  the  horizontal  force. 


^ 

13]  ELASTICITY:     LAWS  OF  STRETCHI 

By  what  two  forces  was  the  cord  acted  upon,  and  in  what 
direction  was  their  resultant  ?  Which  one  of  these  two  forces  was 
measured  directly?  Find  the  value  in  Ibs.  of  the  other  force. 
(As  the  two  forces  are  at  right  angles,  this  may  be  done  either 
graphically  by  constructing  a  triangle  of  forces,  or  by  calculation 
from  similar  triangles.)  Find  also  the  tension  in  the  inclined  part 
of  the  cord. 

VII.    Repeat  VI,  drawing  the  cord  two  feet  to  one  side  instead 
of  one  foot  and  find  again  the  value  of  the  weight. 
,   VIII.    If  three  forces  are  in  equilibrium  about  a  point,  show  that 
they  may  be  represented  in  magnitude  and  direction  by  the  three 
sides  of  a  triangle  taken  in  order. 

13.     ELASTICITY:     LAWS    OF   STRETCHING. 

I.  (a.)  Attach  a  spring  balance  to  the  finer  of  the  wires  hang- 
ing freely  from  the  ceiling.       Set  the  scale   immediately  behind 
this  wire  and  adjust  the  index  on  the  wire,  if  necessary,  until  this 
index  is  opposite  the  upper  part  of  the  scale,  and  read  its  position 
on  the  scale  by  means  of  a  lens,  taking  care  that  the  index,  lens, 
and  eye  are  in  a  horizontal  line.     Read  the  spring  balance  also. 

(b.)  Hang  on  a  weight —putting  it  gently  into  place — and  re- 
peat (a).  Add  successively  three  other  weights,  noting  the 
index  and  balance  readings  in  each  case. 

(c.')  Remove  the  weights  one  by  one,  taking  the  same  readings 
as  in  (d)  and  (a).  Average  the  corresponding  results  of  (a),  (6), 
and  (£•). 

(d.)  Find  the  length  of  wire  used,  measure  its  diameter  in  four 
places  and  compute  its  mean  cross-section. 

II.  Clamp  the  wire  used  in  I  at  about  midway  its  length  and 
repeat  I,   taking  care  to  use  the  Weights  in  the   same    order  as 
before. 

III.  With  a  wire  of  greater  diameter  but  same  material,  repeat 
I,  noting  the  precautions  of  I  and  II. 

IV.  Make   a  plot  of  the    results,  in  I  with    weights  in  dynes' 


32  ACTION   OF   GRAVITY.  [14 

(453.6  grammes  are  equivalent  to  a  pound  Avoirdupois)  as 
abscissae  and  elongation  of  the  wire  as  ordinates.  What  relation 
do  you  find  to  exist  between  the  stretching  force  and  the  resulting 
elongation  ?  The  statement  of  this  relation  is  known  as  Hooke*  s 
Law. 

V.  (a.)  Show  from  I  and  II  the  relation   between  the  length 
and  elongation. 

(£.)  From  land  III,  show  the  relation  between  the  diameter 
and  elongation;  between  the  cross-section  area  and  elongation. 

(c.)  Form  an  equation  giving  the  elongation  in  terms  of  length, 
cross-section,  force  applied,  and  a  constant  K. 

VI.  Stress    is    defined    as  force    per  unit    area;    strain    is    the 
elongation    per   unit   length;    and   the    measure    or   modulus   of 
elasticity  is  the  ratio  of  the  stress  to  the  strain.       Find  the  ex- 
pression for  the  modulus  of  elasticity  in  terms  of  the  quantities  in 
V  and  calculate  its  value  in  C.  G.  S.  units  for  the  substance  used. 
What  relation  exists  between  the  modulus    M   (called    Young's 
Modulus)  and  the  constant  K  in  V  (c)  ?     Is  the  value  of  M  the 
same  for  all  substances?     (Compare  results  with  your  neighbors' 
who  used  wires  of  different  material. ) 

VII.  If  a  very  considerable  weight  were  hung  on  a  wire,  would 
the  conclusions  of  IV,  V,  and  VI  hold?       Explain.     Why  does 
no  correction  have  to  be  made  for   the  position  of  the   spring- 
balance  ? 

14.     ACTION    OF   GRAVITY. 

I.  (a.)  Find  the  time  of  a  quarter- vibration  by  counting  and 
timing  100  complete  vibrations  of  a  rod  pendulum  freed  from  any 
weights  that  may  have  been  attached  to  it. 

(£.)  Fasten  a  strip  of  impression  paper,  dark  side  out,  and  on 
it  a  piece  of  white  paper,  to  the  lower  end  of  the  pendulum. 
Suspend  a  metal  ball  by  a  thread  passing  over  two  nails  above  the 
pendulum,  another  at  the  base,  and  attach  to  the  lower  end  of  the 
pendulum,  pulling  the  latter  aside.  The  weight  of  the  ball  and 


14]  ACTION    OF    GRAVITY.  33 

friction  will  be  sufficient  to  hold  the  pendulum  aside.  Burn  the 
string  near  the  ball  after  it  is  at  rest  and  find  by  trial  to  what 
height  the  ball  must  be  raised  so  as  to  hit  the  paper  when  falling. 
Make  three  determinations  of  this  distance,  measuring  from  the 
center  of  the  ball  above  to  the  corresponding  mark  on  the  paper 
in  each  case. 

II.  Clamp  the  weight  provided  to  the  pendulum  near  the  lower 
end  at  the  place  marked  and  repeat  I  (a)  and  (£). 

III.  Repeat    with    the  weight    clamped    near   the   top  of  the 
pendulum. 

IV.  («.)   Find  in  each  of  the  above  cases,   for  the  time  of  a 
quarter  vibration,   the  average  velocity  of  the  ball,   and  its  final 
velocity.       Show    that    the   final    velocity    is    twice    the    average 
velocity  if  the  ball  starts  from  rest  and  increases  its  velocity  at  a 
constant  rate. 

(£.)  Deduce  from  the  results  of  I,  II,  and  III  the  relation 
between  the  space  passed  over  by  the  ball  and  the  time,  indicat- 
ing clearly  the  process  you  use. 

(/-.)  Calculate  the  distance  the  ball  would  have  passed  over  in 
one  second,  averaging  the  results  of  I,  II,  and  III. 

(d. )  Show  to  what  power  of  the  time  the  acquired  velocity  is 
proportional;  see  (a)  and  (c). 

(<?.)  Calculate  the  velocity  acquired  in  one  second,  i.  e.,  the 
acceleration  (usually  denoted  by  the  letter  g) ,  averaging  results  as 
before. 

V.  («.)  Express  IV  (£)  in  the  form  S=Ktx  and  calculate  the 
value  of  the  constant  K.     What  relation  does  it  bear  to  the  value 
of  g  ?     What  then  is  the  equation  for  the  space  passed  over  in 
terms  of  the  time  and  acceleration  ? 

(b. )  Similarly  find  the  value  of  the  constant  in  the  relation  found 
in  IV  (d)  and  write  the  corresponding  equation. 

(c.)  Deduce  the  expression  for  the  velocity  of  a  body,  starting 
from  rest  and  moving  under  the  action  of  gravity,  in  terms  of  the 
acceleration  and  space. 
3 


34  THE    PENDULUM.  [15 

VI.  If  a  ball  of  greater  mass  had  been  used,  would  the  same 
results  have  been  obtained  for  the  final  velocities  and  for  the 
acceleration?  Explain. 

Distinguish  between  mass  and  weight. 

15.   THE    PENDULUM.     I. 

I.  (a.)  With  a  metal  ball  attached  to  the  longest  wire  that  the 
apparatus  allows,  pulling  aside  the  bob  not  more  than  iocm., 
find  the  period  of  the  pendulum  to  o.oi  second  by  the  following 
method: — 

First  find  the  approximate  period*  by  timing  about  twenty 
vibrations.  (Be  careful  to  count  "one"  when  the  bob  passes  the 
middle  of  the  swing  at  the  end  of  the  first  vibration.)  Next  note 
the  time  that  the  bob  passes  to  the  right  (say)  through  the  center 
of  swing,  the  eye  being  in  line  with  this  position;  wait  about  three 
minutes  and  note  again  the  time  of  transit  in  the  same  direction; 
repeat  this  timing  two  or  three  times.  Between  each  pair  of 
observations  there  was  a  whole  number  of  vibrations.  Divide 
the  first  interval  by  the  approximate  period  found  above;  if  this 
period  were  the  true  one  the  quotient  would  be  an  integer. 
Divide  the  interval  by  the  nearest  integer  to  the  quotient  last 
found  and  the  result  will  be  a  closer  approximation  to  the  true 
period.  Repeat  this  operation  for  the  other  observed  intervals 
and  take  the  mean  as  the  best  value  for  the  period.  (Note: 
The  computations  may  be  done  after  the  whole  experiment  has 
been  performed.)  Measure  the  length  of  the  pendulum,  i.  e., 
from  point  of  suspension  to  center  of  ball. 

(£.)  Repeat  (a),  pulling  aside  the  bob  not  more  than  5  cm. 

(<:.)   Repeat  (a),  pulling  aside  the  bob  some  50  cm. 

(d.)  What  is  the  effect  of  increasing  the  amplitude  on  the 
period  of  a  pendulum  ?  Which  is  the  best  value  to  take  for  the 
period,  that  given  by  (a),  (£),  or  (<;)?  Why? 


*The  period  is  the  time  of  a  complete  vibration,  or  the  time  between 
two  successive  transits  in  the  same  direction. 


16]  THE   PENDULUM.  35 

II.  (<2.)   Repeat    I   (a)  or  (b),   using-   two  shorter    pendulum 
lengths. 

(£.)  Substitute  a  wooden  ball  of  same  size  as  the  metal  one 
and  repeat,  using  any  length  of  pendulum,  but  measuring  it. 

III.  (a.}   From  I  and  II  (a)  find  the  relation  existing  between 
the  length  and  period  of  the  pendulum.      Indicate  clearly  your 
method. 

(<£.)  Show  whether  or  not  the  relation  III  (a)  applies  to  II  (£). 
What  is  the  effect  on  the  period  of  changing  the  mass  of  the 
bob? 

IV.  From  the  results  of  I  and  II  and  the  relation  of  III  (a) 
calculate  the  length  of  the  seconds  pendulum  at  Berkeley.      (A 
seconds  pendulum  is  one  whose  half-period  is  one  second.) 

16.    THE  PENDULUM.     II. 

I.  (a.)  Find  the  period  of  the  pendulum,  to  a  hundredth  of  a 
second,  when  set  so  that  it  vibrates  in  a  vertical  plane.  (See 
Ex.  15.) 

(<£.)  Find  the  period  when  the  plane  of  vibration  makes  an 
angle  of  60°.  35  with  the  vertical,  (cos.  60°.  35=0. 49.) 

(c.)  Find  the  period  when  the  plane  of  vibration  makes  an 
angle  of  75°. 5  with  the  vertical,  (cos.  75°. 5=0.25.) 

(d,}  What  is  the  vertical  force  acting  on  the  pendulum  bob? 
What  is  the  vertical  force  acting  on  unit  mass  of  the  bob? 
Suppose  this  vertical  force  acting  on  unit  mass  to  be  resolved  into 
two  components,  one  perpendicular  to  the  plane  of  vibration  of 
the  pendulum,  and  the  other  in  the  direction  of  its  length  when 
at  rest.  If  a  pendulum  is  constrained  to  vibrate  in  a  particular 
plane,  as  in  this  case,  would  a  force  perpendicular  to  its  plane  of 
vibration  affect  its  period  or  not?  Why?  Draw  a  diagram 
showing  forces  acting  on  bob. 

What  is  the  ratio  between  the  force  per  unit  mass  in  the 
direction  of  the  length  of  the  pendulum  in  (#)  to  that  in  (<£);  in 
(#)  to  that  in  (^)?  (Express  these  ratios  as  reciprocals.)  What 


36  RESONANCE   TUBE.  [17 

is  the  ratio  of  the  period  in  (a)  to  that  in  (£);  in  (a)  to  that  in 
(r)?  (Calculate  these  ratios  in  decimals.)  By  comparing  these 
results,  find  the  law  connecting  the  period  of  a  pendulum  with  the 
force  on  unit  mass,  or  the  acceleration,  in  the  direction  of  its 
length  when  at  rest,  assuming  that  the  period  varies  as  some 
integral  root,  or  power,  of  the  acceleration. 

II.  (To  be  done  when  Ex.  15  has  been  completed.)     (a.)   From 
the    law   deduced    in  III   (a)   of  Ex.   15  find  the  length  of  the 
simple  pendulum  equivalent  to  the  physical  pendulum  of  I  (a), 
Ex.  1 6,  using  the  seconds  pendulum  as  comparison. 

(£.)  Express  the  period  P  of  a  simple  pendulum  in  terms  of  a 
constant  k,  its  length,  L,  and  acceleration  in  the  direction  of  its 
length.  The  latter  quantity  is  g  (see  Ex.  14)  if  the  pendulum 
vibrates  in  a  vertical  plane. 

(f.)  Calculate  the  values  of  g  and  of  k  as  follows:  The  equation 
of  II  (&)  applies  to  the  case  of  the  seconds  pendulum  of  Ex.  15 
and  to  the  simple  pendulum  of  II  (a}.  Form  two  simultaneous 
equations  for  the  values  of  k  and  g  in  terms  of  the  known  quanti- 
ties L  and  P,  for  each  pendulum,  and  solve  fork  and  g. 

III.  Is  the  length  of  the  seconds  pendulum  the  same  over  the 
surface  of  the  earth?     Why  ?     Write  not  less  than  one  hundred 
words  on  the  uses  of   the  pendulum. 

17.    RESONANCE   TUBE. 

The  resonance  tube  to  be  used  consists  of  a  long  vertical  glass 
tube  connected  at  its  lower  end  by  a  rubber  tube  and  siphon  with 
a  jar  of  water,  so  that  when  the  jar  is  raised  and  lowered,  the 
water  flows  in  and  out  of  the  tube.  The  siphon  can  be  started 
by  setting  the  jar  on  the  floor  and  pouring  water  into  the  tube 
until  it  flows  into  the  jar.  The  water  in  the  tube  may  be  kept  at 
any  desired  level  by  turning  the  cock  at  the  base. 

Tuning  forks  are  to  be  set  in  vibration  by  striking  with  rubber 
hammer,  and  in  no  other  way. 

I.    Hold  a  vibrating  A-fork  over  the  nearly  full  tube,  and  mark 


17]  RESONANCE   TUBE.  37 

with  a  rubber  band  as  the  jar  is  lowered  the  level  of  the  water 
when  the  air  in  the  tube  vibrates  in  unison  with  the  fork  and 
causes  a  marked  increase  in  the  intensity  of  the  sound. 

Raise  the  jar,  and  as  the  water  rises  readjust  the  rubber  band 
to  the  level  of  the  water  when  the  sound  swells  out  again.  Let 
the  water  rise  and  fall  past  this  point  a  number  of  times  and 
determine  the  level  when  the  air  in  the  tube  vibrates  in  unison 
with  the  fork,  as  accurately  as  you  can,  recording  each  measure- 
ment. 

As  the  air  has  no  freedom  of  motion  in  a  vertical  direction  at 
the  surface  of  the  water,  this  plane  where  the  column  of  air  may 
be  cut  off  without  prejudice  to  its  rate  of  vibration  must  be  one 
of  minimum  vibration,  i.  e.,  a  nodal  plane. 

What  is  the  condition  of  the  air  at  the  open  end  of  the  tube  ? 

Find  all  the  prominent  nodal  planes  you  can.  Measure  the 
distances  between  them  and  between  the  highest  one  and  the 
open  end  of  the  tube.  Is  the  latter  the  same  as  the  distance 
between  two  consecutive  nodal  planes  ?  Can  you  account  for  the 
fact  that  the  ratio  of  these  distances  is  not  exactly  1:2?  How 
are  these  distances  related  to  the  wave-length  in  air  of  the 
particular  note  sounded  ?  Explain  and  draw  diagram  in  illustra- 
tion. 

II.  Repeat  I  with  the  two  C-forks,  and  also  with  a  G-  or  D- 
fork. 

Find  the  ratio  of  the  distance  between  the  nodes  when  the 
A-fork  was  used  to  that  when  the  large  C-fork  was  used.  This 
gives  the  ratio  between  the  wave-lengths.  How  is  this  ratio 
related  to  the  ratio  between  the  vibration  frequencies  of  the  two 
notes?  The  latter  ratio  measures  the  musical  interval  between 
the  notes. 

Calculate  from  your  results  the  musical  intervals  between  the 
lower  C-fork  and  each  of  the  others. 

III.  If  the  larger    C-fork  makes  256  complete  vibrations  per 
second,  calculate  the  velocity  of  sound  in  air  in  the  tube  used. 
Find  the  vibration  number  of  each  of  the  other  forks. 


38  VELOCITY    OF   SOUND    IN    SOLIDS.  [l8 

IV.    Explain  why  the  column  of  air  emits  a  note. 
Is  more  or  less  energy  used  by  the  fork  and  air  column  sound- 
ing together  than  when  the  fork  is  sounding  alone?     Explain. 

18.     VELOCITY   OF   SOUND    IN    SOLIDS. 

I.  Clamp  a  long  brass  rod  exactly  at  its  middle  point  in  a  vice. 
Take  a  long  glass  tube,  provided  with  a  piston  at  one  end  and 
containing    powdered    cork,    and    set    its    rubber-covered    end 
against  one  end  of  the   rod.      A  cardboard  disc  of   some  -2  cm. 
diameter  should  be  glued  to  this  end  of  the  rod. 

Set  the  rod  in  vibration  by  stroking  it  from  the  center  out 
slowly  and  with  but  slight  pressure,  with  a  cloth  wet  with  wood 
alcohol  or  rubbed  with  resin.  The  piston  should  be  adjusted  by 
trial  until  the  cork-dust  takes  up  its  characteristic  arrangement. 
Describe  the  behavior  of  the  cork  dust.  Where  are  the  nodes  ? 
The  loops?  Which  is  found  at  either  end  of  the  tube ?  Explain. 
Measure  the  length  of  the  tube  and  find  the  wave-length  of  the 
sound  in  air.  What  is  the  wave-length  of  the  sound  in  the  rod? 
Explain.  Make  three  determinations. 

Calculate  the  ratio  of  the  wave-length  in  brass  to  the  wave- 
length in  air  for  the  same  note.  How  is  this  ratio  related  to  the 
relative  velocity  of  sound  in  brass  and  air?  Calculate  the  velocity 
of  sound  in  brass,*  and  write  out  the  equations  involved. 

II.  Repeat  the  measurements  of  I  with  a  glass  rod  and  find  the 
velocity  of  sound  in  glass. 

III.  Repeat  with  an  iron  rod. 

IV.  How  with  this  apparatus  might  the  velocity  of  sound  in 
gases  be  found?     Write  the  equations  involved. 

V.  Write  at  least  one  hundred  words  on  the  subject  of  station- 
.  ary  waves. 


*The  velocity  of  sound  in  air  is:— 

V=33i  i/  1+0.0041  metres  per  second,  where  t  is  the  temperature  in 
centigrade, 


19]  LAWS   OF   A    VIBRATING    STRING.  39 

19.     LAWS   OF  A   VIBRATING   STRING. 

I.  (#.)     Attach    two    piano   steel  wires  (No.   27  and  No.    22 
B.  &  S.  gauge)  to  a  sonometer  and  stretch  the  lighter  wire  over 
the  sounding-board  with  a  weight  of  4  Ibs.       Move  the  sliding 
bridge  until  the  note  given  out  by  the  wire  when  plucked  is  in 
unison  with  the  tuning-fork  provided.     (The  note  of  the  fork  can 
be  made  more  audible  by  holding  the  end  of  its  handle  on  the 
sonometer  board. )     Measure  the  length  of  the  vibrating  part  of 
the  wire. 

(&.)  Move  the  sliding  bridge  so  that  the  note  given  out  by  the 
wire  is  in  unison  with  the  note  an  octave  *  below  that  of  the 
tuning-fork,  and  again  measure  the  vibrating  part  of  the  wire. 

(<:.)  What  is  the  relation  between  the  vibration  frequency  of 
two  notes  separated  by  an  interval  of  an  octave?  What,  by 
comparing  the  results  of  («)  and  ($),  do  you  find  to  be  the  law 
connecting  the  length  of  the  vibrating  wire  (or  string)  with  its 
vibration  frequency? 

II.  With  additional  weights  increase  the  tension  of  the  wire  to 
four  times  its  tension  in  I,  and  adjust  the  sliding  bridge,  if  neces- 
sary, so  that  the  note  given  out  is  in  unison  with  that  of  the  tun- 
ing-fork.     How  does  the  length  of  the  vibrating  part  of  the  wire 
compare  in  this  case  with  its  length  in  I  (b)  ?     What  do  you  con- 
clude   to    be    the   law    connecting    the  vibration  frequency  of  a 
stretched  wire  with  its  tension  ? 

III.  (a.)  Repeat  the  experiment  of  I  with  the  heavier  wire,  and 
by  comparison  with  the  result  of  I  (a}  find  the  ratio  between  the 
lengths  of  the    two  wires   when    their  vibration  frequencies    are 
equal.     From  this  find  the  ratio  between  the  vibration  frequencies 
of  the  two  wires  when  their  lengths  are  made  equal  ?     (See  law 
found  in  I.) 

(b.)  Measure  the  length  of  a  piece  of  each  kind  of  wire  and  find 
the  ratio  of  their  masses  per  unit  length,  using  a  Jolly  balance  for 
weighing. 

*  Two  notes  have  an  interval  of  an  octave  where  one  has  twice  the 
pitch  of  the  other. 


40  PHOTOMETRY.  [20 

What  do  you  find  to  be  the  relation  between  the  vibration 
frequency  and  linear  density  of  a  stretched  wire,  the  length  and 
tension  being  constant? 

IV.  Form  an  expression  for  the  pitch  of  a  wire  in  terms  of  its 
length,  tension  and  linear  density.  What  does  this  equation 
assume  regarding  the  elastic  properties  of  the  wire  and  the  nature 
of  its  motion? 

20.  PHOTOMETRY. 

I.  Set  a  diffusion  photometer,  —  two  rectangular  blocks  of  paraf- 
fine  separated  by  a  sheet  of  tin-foil, — so  that  the  two  blocks  of 
paraffine  are  equally  illuminated  by  the  diffused  light  of  the  room. 
Light  a  set  of  four  simple  gas  jets  and  a  single  separate  jet  of  the 
same  form,  and  regulate  the  flow  of  gas  so  that  the  jets  are  all  of 
the   same    height    and    brightness.       Place    the    single   jet   at    a 
distance  of  50  cm.   on    one    side  of  the    photometer,    so  as    to 
illuminate  one  block  of  the  paraffme,  and  the  set  of  four  jets  on 
the  other  side  at  such  a  distance  that  the  two  blocks  of  paraffine 
will    be    equally   illuminated.       Measure    the    distance    from    the 
photometer  to  the  four  jets. 

How  does  the  illumination  of  the  paraffine  due  to  the  single  jet 
compare  with  that  due  to  the  four  jets?  How  does  the  intensity 
of  the  illumination  due  to  a  single  jet  at  50  cm.  compare  with 
that  due  to  a  single  jet  at  the  distance  of  the  four  jets  ?  The 
intensity  of  the  illumination  is  proportional  to  an  integral  power 
of  the  distance;  what,  from  your  results,  do  you  conclude  the 
power  in  question  to  be?  Is  it  direct  or  inverse? 

II.  Place  the  four  jets  at  50  cm.  from  the  photometer  and  the 
single  jet  on  the  opposite  side  at  such  a  distance  that  the  blocks 
of  paraffine  are  again  equally  illuminated.       Are  the  conclusions 
drawn  from  the  results  of  I  corroborated,  or  not,  by  the  results 
thus  obtained  ?     Record  measurements. 

III.  Light  a  candle  and  place  it  at  a  certain  distance  from  the 
photometer.      Light  a  coal-oil  lamp  and  place  it  on  the  opposite 
side  of  the  photometer,   so  that  the  candle  and  lamp  illuminate 


21]  REFRACTION.  41 

the  blocks  of  paraffine  equally.  (The  height  of  the  lamp  wick 
should  not  be  altered  during  the  course  of  this  experiment,  and 
the  lamp  should  burn  at  least  five  minutes  before  taking  read- 
ings.) How  can  you  find  the  ratio  between  the  illuminating 
power  of  the  candle  and  that  of  the  lamp  ?  (Take  four  readings 
with  varying  distances  of  the  candle.)  What  is  this  ratio  as 
derived  from  your  measurements? 

Weigh  the  lamp  and  the  candle.  Let  them  burn  for  30 
minutes.  Reweigh  and  find  the  mass  of  the  coal-oil  and  of  the 
paraffine,  or  candle  substance,  consumed.  For  one  gramme  of 
matter  consumed  by  the  candle,  how  many  grammes  were  con- 
sumed by  the  lamp  ?  Calculate  the  relative  illuminating  power  of 
coal-oil  and  paraffine  for  equal  masses  consumed,  assuming  that 
the  illuminating  power  varies  directly  as  the  amount  of  matter 
consumed. 

IV.  Alter   the    height   of    the    lamp    flame   and    repeat    III. 
Calculate  again,  from  the  result  obtained,  the  relative  illuminating 
power  of  coal-oil  and  paraffine  for  equal  masses  consumed.     How 
does  the  value  found  compare  with  that  found  in  III?       Is  the 
assumption    made    above,    that    the    illuminating    power    varies 
directly  as  the  amount  of  matter  consumed,  corroborated  by  the 
results  of  III  and  IV,  or  not? 

V.  Form    an    equation    expressing    the  candle    power  of  any 
source  of  light  in  terms  of  the  proper  variables.       Distinguish 
between  intensity  of  illumination  and  illuminating  power. 

21.    REFRACTION. 

I.  Take  a  rectangular  cell,  having  one  side  of  plate  glass  and 
containing  a  mirror  revolving  on  a  vertical  axis,  and  fill  it  about 
half  full  of  water.  Set  this  cell  so  that  the  axis  on  which  the 
mirror  revolves  is  over  the  center  of  a  large  circle  drawn  on  the 
table.  Adjust  the  cell  so  that  its  glass  side  is  perpendicular  to  2t 
radius  of  the  circle  drawn  parallel  to  the  end  of  the  table.  This 
may  be  done  by  stretching  a  white  string  along  this  radius,  and 


42  REFRACTION.  [21 

moving  the  cell  until  the  image  of  the  string  in  the  plate  glass 
coincides  in  direction  with  the  string  itself.  (A  piece  of  blackened 
tin  held  back  of  the  plate  glass  will  help  in  locating  the  image  of 
the  string.) 

Move  your  eye  along  the  edge  of  the  table  until  you  see  the 
image  of  the  string  in  the  mirror  above  the  water.  With  another 
white  string  locate  the  direction  of  this  image,  and  stick  a  pin  in 
line  with  it  on  the  circle  drawn  on  the  table.  In  the  same  way 
look  for  the  image  of  the  string  seen  through  the  water,  and  mark 
with  another  pin  on  the  circle  the  direction  of  this  image. 

Measure  the  perpendicular  distance  from  each  of  these  pins  to 
the  radius  represented  by  the  first  string. 

Answer  the  following  questions: — 

1.  Does  the  light  from  the  first  string  undergo  any  change  in 
direction  on  entering  the  cell  ? 

2.  Will  it,  therefore,  strike  the  mirror  at  the  same  angle  within 
the  liquid  as  without,  i.  e. ,  above  the  liquid  ? 

3.  Will  it  be  reflected  at   the  same  angle  within  as  without  the 
liquid  ? 

4.  Will  the  reflected  light,  passing  through  the  liquid,  have  the 
same    direction  after  leaving  the  liquid  as   that  which   does  not 
pass  through  the  liquid?     What  do  you  find  by  experiment  ? 

Remembering  that  the  first  string  is  perpendicular  to  the  sur- 
face of  the  water  at  which  the  light  is  refracted,  how  are  the 
sines  of  the  angles  of  incidence  and  refraction  related  to  the 
distances  measured  above? 

The  ratio  of  the  sine  of  the  angle  of  incidence  to  that  of  refrac- 
tion when  the  light  is  incident  in  air,  or,  more  properly,  in  a  vac- 
uum, is  called  the  index  of  refraction  of  the  substance.  (If  the 
light  is  incident  in  the  substance  and  refracted  in  air,  the  index  of 
refraction,  on  the  contrary,  is  equal  to  the  ratio  of  the  sine  of  the 
angle  of  refraction  to  that  of  the  angle  of  incidence.)  Calculate 
from  your  results  the  index  of  refraction  of  water. 

II.  Repeat  I  with  the  mirror  at  a  slightly  different  angle  and 
calculate  again  the  index  of  refraction  of  water. 


22]  REFRACTION    AND    DISPERSION.  43 

III.  Rotate  the  mirror  a  little  more  and  repeat  I,  calculating 
again  the  index  of  refraction. 

Do  you  find  the  index  of  refraction  to  vary  with  the  angle  of 
incidence,  or  not  ? 

IV.  Take    a    cubical    block  of  glass  and   lay  it  on  a  sheet   of 
brown    paper.      Mark   on    the  paper  the  position  of  two  of  its 
opposite  edges,  and  continue  the  lines  with  a  ruler  held  against 
the  face  of  the  cube.     Stick  a  pin  in  the  table  about  30  cm.  from 
the   cube,  and  as    far    to  one  side  as  it   can   be  placed  without 
becoming  invisible  when  looked  at  diagonally  through  the  oppo- 
site faces  of  the  cube.      Looking  at  this   pin  through  the  cube, 
place  three  pins  in  line  with  it,  one  on  the  same  side  close  to  the 
cube,  and  two  on  the  side  of  the  observer.      Remove  the   cube 
and  draw  lines  on  the  paper  to  show  the  direction   of  the  light 
from  the  first  pin  before  entering  the  glass,  after  passing  through 
the  glass,  and  within  the  glass.      How  did  the  direction  of  the 
light  before  entering  the  glass  cube    compare  with  its  direction 
after  passing  through  the  cube  ? 

Draw  a  perpendicular  to  the  face  of  the  cube  through  the  point 
where  the  light  entered,  make  the  proper  measurements,  and  cal- 
culate the  index  of  refraction  of  the  glass.  Turn  the  cube  through 
1 80°  and  repeat. 

V.  How    with    the    rectangular    cell,  if  the  dimensions  of  the 
apparatus  permitted,  might  the  critical  angle  for  water  be  found  ? 
Explain,  giving  a  diagram. 

22.    REFRACTION    AND    DISPERSION. 

I.  Set  a  mirror  in  a  small  rectangular  cell,  and  fill  it  about  half 
full  of  water.  Place  the  cell  with  its  glass  side  perpendicular  to 
the  line  formed  by  a  linear  source  of  light  (an  electric  lamp  with 
' '  hofseshoe ' '  filament)  and  a  narrow  slit  and  at  a  distance  of 
100  cm.  from  the  scale  of  a  metre  rod  set  at  right  angles  to  the 
line  of  the  light  and  slit.  Move  your  eye  along  the  metre  rod 
until  the  image  of  the  light  in  the  mirror  above  the  water  becomes 


44  IMAGES    IN   A   SPHERICAL   MIRROR.  [23 

plainly  visible  and  read  the  scale.  Look  in  the  same  way  for  the 
image  of  the  light  in  the  mirror  as  seen  through  the  water.  Is 
this  image  similar  in  appearance  to  that  seen  above  the  water  ? 
Describe  and  explain  the  difference.  Can  you  locate  its  direction, 
as  was  done  for  the  image  seen  above  the  water  ? 

Locate  the  direction  of  the  extreme  red  of  the  spectrum  seen 
through  the  water.  As  the  distance  of  the  scale  from  the  cell  is 
one  metre  (100  cm.),  the  respective  readings  of  the  scale  in 
metres  will  be  equal  to  the  tangents  of  the  angles  of  incidence 
and  refraction.  The  source  of  light  may  be  considered  as  at  the 
surface  of  the  mirror,  hence  the  light  is  incident  in  the  dense 
medium.  Show  by  diagram  the  angles  of  incidence  and  refrac- 
tion. Using  a  table  of  natural  sines  and  tangents,  find  the  sines 
corresponding  to  these  tangents,  and  calculate  the  index  of 
refraction  of  water  for  red  light.  (See  Expt.  21  for  definition  of 
index  of  refraction.) 

Find  in  the  same  way  the  index  of  refraction  for  blue  light, 
using  the  extreme  blue  of  the  spectrum;  and  also  for  yellow 
light. 

II.  Repeat   I  with  a  saline  solution  instead  of  water.      What 
effect   do    you  find  salt  in  solution   to  have   upon   the   index  of 
refraction  of  water? 

The  angle  between  the  rays  of  red  and  blue  light  after  refraction 
is  called  the  dispersion  for  red  and  blue  light.  What  is  the 
dispersion  for  these  rays  for  water  and  for  the  salt  solution  ? 

III.  Show  how  from  this  experiment  the  velocity  of  light  in  the 
salt  solution  may  be  computed,  if  the  velocity  in  water  is  known, 
and  demonstrate  the  relation  between  the  index  of  refraction  and 
velocity. 

GROUP    III. 

23.    IMAGES    IN  A  SPHERICAL    MIRROR. 

I.  Place  a  concave  spherical  mirror  so  as  to  form  as  clear  an 
image  as  possible  of  the  window-sash  on  a  screen,  and  measure 
the  distance  from  the  mirror  to  the  screen. 


23]  IMAGES    IN    A    SPHERICAL    MIRROR  45 

Repeat,  using-  some  distant  object,  as  the  tops  of  the  trees 
across  the  road,  instead  of  the  window-sash,  and  measure  again 
the  distance  from  the  mirror  to  the  screen.  Was  this  distance 
greater  or  less  than  when  the  window-sash  was  focused  on  the 
screen  ?  The  principal  focus  is  the  point  through  which  all 
parallel  rays  are  reflected.  Its  distance  from  the  mirror  is  called 
the  principal  focal  length  of  the  mirror.  Which  of  the  meas- 
urements above  may  be  taken  as  the  principal  focal  length  of  the 
mirror  ? 

II.  Place  an  upright  rod  at  a   distance  in  front  of  the  mirror 
equal  to  twice  its  principal  focal  length.      Adjust  the  position  of 
the  rod  by   the   method  of  parallax,  so  that  some  definite  point 
on  it  will  coincide  in  position  with  its  image  in  the  mirror.      Do 
this    by   adjusting  the  rod    first  so  as  to  coincide  with   its   own 
image*,  and  then  sliding  a  piece  of  paper  up  or  down  the  rod 
until  it  meets  its  image.     This  will  give  the  required  point  on  the 
rod.      (Do    not  confound    the  image  formed  by  the  front,  plane 
surface  of  the  glass  with  that  formed  by  the  spherical  mirror  on 
the    back.)     What    measurement    will    now    give    the    radius   of 
curvature  of  the  mirror  ?     Why  ?     How  does  this  compare  with 
the  principal  focal  length? 

III.  (a.)   Place  the  screen  at  as  great  a  distance  from  the  mirror 
as  the  table  will  allow,  and  place  two  gas  jets  so  that  their  images 
formed  on  the  screen  will  be  as  distinct  as   possible.       To   obtain 
images  beyond  the  center  of  curvature  of  the  mirror,  where  did 
the  gas  jets  have  to  be  placed,  between  the  mirror  and  the  prin- 
cipal focus,  between  the  principal  focus  and  the  center  of  curva- 
ture, or  beyond  the  center  of  curvature? 

(^.)  Measure  the  distance  from  the  mirror  to  the  gas  jets  and 
the  distance  from  the  mirror  to  the  screen;  also  the  distance 
between  the  gas  jets  and  the  distance  between  their  images. 

*This  can  he  done  by  changing  the  position  of  the  observer's  eye  and 
adjusting  and  readjusting  the  position  of  the  rod  until  it  will  always 
coincide  in  direction  with  its  own  image  from  every  point  of  view. 


46  IMAGES   IN   A   SPHERICAL    MIRROR.  [23 

How  does  the  ratio  between  the  first  two  distances  compare  with 
the  ratio  between  the  last  two?  Find  the  ratio  between  the 
distance  of  the  object  and  that  of  its  image  from  the  center  of 
curvature  of  the  mirror  instead  of  from  its  surface.  How  does 
this  ratio  compare  with  the  other  two? 

(Y.)  Reduce  to  decimals  the  reciprocals  of  (i)  the  distance 
from  the  mirror  to  the  gas  jets;  (2)  the  distance  from  the 
mirror  to  their  images;  (3)  the  principal  focal  length;  (4)  the 
radius  of  curvature.  Of  these  four  reciprocals  find  two  whose 
sum  is  equal  to  a  third,  and  also  equal  to  a  simple  multiple  of 
the  fourth. 

IV.  Interchange  the  positions  of  the  gas  jets  and  the  screen. 
(In  the  new  positions  they  will,  of  necessity,  have  to  be  placed  on 
opposite  sides  of  a  line  normal  to  the  mirror.)     Adjust  the  screen 
so    as    to   obtain  as   definite  images  as  possible,  and  repeat   the 
measurements  of  III  (<£).      Does  the  proportion  found  in  III  ($) 
still  hold  true?     Does  the  relation  between  the  reciprocals  in  III 
(Y)  still  hold  true?     When  the  gas  jets  are  beyond  the  center  of 
curvature,  are    the   images  formed   between  the  mirror  and  the 
principal    focus,    between  the  principal   focus  and  the   center  of 
curvature,  or  beyond  the  center  of  curvature? 

V.  Place    a  vertical  rod  between  the  mirror  and  its  principal 
focus,  within  8  or  10  cm.  of  the  mirror,  and  locate  its  image  by 
means  of  another  rod,  using  the  method  of  parallax.      Measure 
the  distance  from  the  mirror  to  the  object  and  its  image  respec- 
tively.      In  order  that  the  relation  between  the  reciprocals  found 
in  III  (Y)  shall  still  hold  true,  what  change  in  sign  is  necessary? 
Write  the  equations  representing  the  conditions  in  III  and  V. 

VI.  Suppose  an  object  at  an  infinite  distance  from  the  mirror; 
where    would  its    image  be  found,  and  how  would  it  change  in 
position    as  the    object    approached  the    mirror,   supposing    the 
object    to  approach    until  it   touched  the  surface  of  the  mirror  ? 
State  whether    the    image    would  be    real,   or    virtual;  erect,  or 
inverted;  larger  than  the  object,  or  smaller. 


24]  CONVEX   LENSES.  47 

24.    CONVEX    LENSES. 

I.  (0.)  With  a  convex  lens  form  an  image  of  the  window-sash 
on  a  screen  and  measure  the  distance  from  the  lens  to  the  screen. 

(<£.)  With  the  same  lens  form  an  image  of  some  distant  object 
on  the  screen,  and  measure  again  the  distance  from  the  lens  to 
the  screen.  Is  this  distance  the  same  as  in  (a)?  Which  of 
these  distances  may  be  taken  as  the  principal  focal  length  of  the 
lens?  Why? 

-II.  Light  two  gas  jets  and  place  them  at  a  distance  from  the 
lens  equal  to  twice  its  principal  focal  length,  and  place  the  screen 
so  as  to  form  as  distinct  images  of  the  jets  as  possible.  Measure 
the  distances  respectively  from  the  lens  to  the  screen,  and  from 
the  lens  to  the  gas  jets.  How  do  these  distances  compare? 
Measure  the  distances  between  the  gas  jets  and  between  their 
images.  How  do  these  distances  compare? 

III.  Set  the  gas  jets  at  a  distance  from  the  lens  equal  to  about 
five  times  its  principal  focal  length,  and  place  the  screen  so  as  to 
form  as  distinct  images  as  possible  of  the  jets. 

Measure  the  distances:  (i)  From  the  lens  to  the  screen;  (2) 
from  the  lens  to  the  gas  jets;  (3)  between  the  gas  jets;  (4) 
between  their  images.  Find  a  relation  existing  between  these 
quantities  and  express  it  in  the  form  of  a  proportion. 

Reduce  to  decimals  the  reciprocal  (i)  of  the  principal  focal 
length;  (2)  of  the  distance  of  either  gas  jet  from  the  lens;  (3)  of 
its  image  from  the  lens.  The  sum  of  what  two  of  these  recipro- 
cals is  approximately  equal  to  the  third? 

IV.  Interchange  the  position   of  the  gas  jets  and  the  screen 
and   adjust  the  lens,  if  necessary,  so  as  to  make  the  images  as 
distinct  as  possible.      Repeat  the  measurements  of  III. 

Form  a  proportion,  if  you  can,  similar  to  that  formed  in  III, 
and  find,  if  you  can,  a  similar  equation  connecting  certain 
reciprocals.  Indicate  any  difference  in  the  two  cases. 

V.  Set  an  upright  rod  between  the  lens  and  the  principal  focus. 
On  which  side  of  the  lens  is  the  image  of  the  rod  ?     Is  the  image 


48  CONCAVE   IvENSKS.  [25 

real,  or  virtual;  erect,  or  inverted?  Locate  this  image  by  means 
of  another  upright  rod,  by  the  method  of  parallax,  (Exercise  23, 
II.)  In  order  that  the  relation  between  the  reciprocals  previously 
found  should  still  hold  true,  what  change  in  sign  is  necessary  ? 

VI.  Answer  the  following  questions  as  applied  to  a  convex  or 
converging  lens: — 

1 .  Where  should  an  object  be  placed   in   order  that  its  image 
may  be  real?     In  order  that  its  image  may  be  virtual? 

2.  When  will  the  image  be  erect,  and  when  inverted  ? 

3  Where  should  the  object  be  placed  in  order  to  form  an 
enlarged  image?  In  order  to  form  a  diminished  image? 

4.  Where  should  the  object  be  placed  in  order  to  use  a  con- 
verging lens  as  a  magnifying  glass? 

25.     CONCAVE    LENSES. 

I  Locate  with  an  upright  rod  the  image  formed  by  a  concave 
lens  of  some  vertical  part  of  the  window-sash,  using  the  method 
of  parallax.  (Exercise  23,  part  II.)  (The  rod  used  in  locating 
the  image  should  be  looked  at  over,  not  through,  the  lens.) 
Measure  the  distance  from  the  lens  to  the  image. 

Locate  in  the  same  way  the  image  of  some  vertical  object  in 
the  distance,  as  the  corner  of  a  house,  or  a  telegraph  pole,  and 
find  the  principal  focal  length  of  the  lens.  Explain. 

II.  («.)  Place  the  vertical  rod  at  a  distance  from  the  lens  equal 
to  about  twice  its  principal  focal  length,  and  locate  its  image  by 
means  of  another  vertical  rod.  Measure  the  distance  from  the 
lens  to  the  image. 

(£.)   Repeat  with  the  stationary  rod  at  the  principal  focus. 

(c.)  Repeat  with  the  stationary  rod  between  the  principal  focus 
and  the  lens. 

Reduce  to  decimals  the  reciprocal:  (i)  of  the  distance  from  the 
lens  to  the  image  in  either  (a),  (£),  or  (c);  (2)  of  the  corre- 
sponding distance  from  the  lens  to  the  object;  (3)  of  the  princi- 
pal focal  length.  Which  one  of  these  distances  should  be  made 


25]  CONCAVE   LENSES.  49 

negative  in  order  that  the  sum  of  the  first  two  reciprocals  should 
be  equal  to  the  third  ? 

III.  Set  two  vertical  rods  attached  to  the  same  support  at  a 
suitable  distance  from  the  lens  (to  be  determined  by  the  student), 
and  locate  their  images  by  means  of  two  other  separate  rods. 

Measure  (i)  the  distance  of  the  fixed  pair  of  rods  from  the  lens, 
(2)  the  distance  of  their  images  from  the  lens,  (3)  the  distance 
between  the  rods,  and  (4)  the  distance  between  their  images. 
Find  the  relation  existing  between  these  four  quantities  and  ex- 
press it  in  the  form  of  a  proportion,  and  state  it  in  words. 

IV.  Answer  the  following  questions: — 

1 .  Can  a  real  image  be  formed  by  a  concave  lens  ? 

2.  Can  a  concave  lens  be  used  as  a  magnifying  glass? 

3.  Suppose  an  object  at  an    infinite    distance  from  a  concave 
lens;  where  would  its  image  be  located,  and  how  would  it  change 
in  position    as    the  object    approached    the    lens,   supposing   the 
object  to  approach  until  it  touched  the  lens  ? 

4.  Can  there  be,  when  a  single  lens  or  mirror  is  used,  such  a 
thing  as  a  real  and  erect  image,  or  a  virtual  and  inverted  image? 

V.  *  When  Exercises  23-25  have  been  done,  copy  and  fill  out 
the  following  table. 

VI.  Also  construct  geometrically  the  following:— 

(i.)  The  image  of  an  object  within  the  focus  of  a  concave 
mirror. 

(2.)  The  image  of  an  object  at  the  center  of  curvature  of  a 
diverging  lens. 

(3.)  The  image  of  an  object  between  the  focus  and  center  of 
curvature  of  a  converging  lens. 

Demonstrate  that  to  produce  a  real  image  with  a  converging 
lens  the  object  and  image  must  be  separated  by  a  distance  of 
at  least  4/~. 

VII.  Write  what  you  can  of  the  analogies  between  a  concave 
mirror  and  a  converging  lens,  between  a  convex  mirror  and  a 
diverging  lens. 


*  Parts  V  and  VI  and  VII  may  be  handed  in  as  a  separate  exercise. 
4 


CONCAVE   LENSES. 


CONCAVE 
MIRROR. 

CONVEX 
LENS. 

CONCAVE 
LENS. 

D—co 

Magnified  or  diminished 

- 

Location  of  Image  

00  >  D>  2f 

Real  or  virtual 

Magnified  or  diminished 

Location  of  Image 

D—yf 

Magnified  or  diminished 

2f>  D  >  f 

Real  or  virtual        

Magnified  or  diminished 

Location  of  Image 

f>  D~>  o 

Real  or  virtual 

/}=Distance  of  object  from  mirror. 
/=Principal  focal  length. 


26]  DRAWING    SPECTRA.  51 

26.     DRAWING   SPECTRA. 

The  spectroscope  should  be  examined  and  its  construction 
understood  before  proceeding.  The  instrument  should  be  set  so 
that  the  slit  in  the  collimator  does  not  point  toward  any  outside 
source  of  light,  as  a  window.  The  instrument  may  be  adjusted 
for  use  as  follows:  Place  a  colorless  Bunsen  flame,  in  which  is 
held  asbestos  soaked  with  salt  solution,  directly  before  the  slit  and 
narrow  the  latter,  focusing  upon  it  with  the  telescope,  the 
prism  being  in  place,  until  the  slit  appears  as  a  sharp,  bright  line. 
Light  the  gas  illuminating  the  scale  in  the  third  arm  of  the 
instrument,  and  focus  the  scale  by  moving  it  in  and  out  until  the 
figures  upon  it  can  be  distinctly  read.  (The  eye-piece  should  not 
be  touched  during  this  last  operation.)  Bring  the  5  (or  50) 
mark  of  the  scale  into  coincidence  with  the  yellow  line  due  to 
the  sodium.  If  now  the  adjustment  has  been  carefully  done,  by 
moving  the  eye  slightly  back  and  forth  before  the  eye-piece  the 
sodium  line  and  the  mark  5  will  not  appear  to  move  with  respect 
to  each  other.  If  there  is  such  motion  repeat  the  adjustment. 

I.  The  spectra  of  the  salts  provided   are  to  be  examined  and 
drawn  upon  plotting  paper,  the  spectroscope  scale  being  plotted 
as  abscissae   and  each   spectrum  on  a  separate   horizontal   line. 
(See  sample  note-book.)     State  in  each  case  the  general  color 
of  the  flame  and  the  colors  of  the  various  lines  and  bands. 

To  observe  successfully  the  potassium  spectrum  it  will  be  nec- 
essary to  open  the  slit  somewhat  and  insert  a  piece  of  cobalt 
glass  between  the  flame  and  the  slit.  The  sodium  spectrum  will 
probably  be  ever  present,  but  is  readily  distinguished  from  that  of 
the  salt  under  examination. 

II.  Draw  the  spectrum  of  a  luminous  flame,  and  also  of  the 
same  flame  seen  through  red,  green,  yellow,  and  blue  glass.     Is 
the   light  transmitted    by    any  of  these  glasses  monochromatic? 

Distinguish  between  absorption  spectra  and  emission  spectra. 

III.  The  wave-lengths  corresponding  to  certain  spectral  lines 
are  furnished;  draw  a  smooth  curve  in  terms  of  their  position  on 


52  LAWS    OF    MAGNETIC    ACTION.  [27 

the  scale  and  from  this  curve  determine  the  wave-lengths  corre- 
sponding to  the  calcium  lines  and  the  strontium  lines. 

IV.  Draw  a  diagram    representing    the  optical    principles    in- 
volved in  the  construction  and  use  of  the  spectroscope  you  used. 

V.  Write  not  less  than  one  hundred  words  on  the  uses  of  the 
spectroscope. 

27.     LAWS   OF    MAGNETIC    ACTION. 

Prove  that  if  a  compass-needle  is  deflected  by  a  horizontal  force 
acting  in  an  east  and  west  direction,  the  magnitude  of  the  force 
will  be  proportional  to  the  tangent  of  the  angle  of  deflection. 

I.  Place  two  pocket  compasses  side  by  side.     Do  the  like  poles 
attract  or  repel  each  other?     Do  the  unlike? 

II.  Lay  a  compass  on  a  large  sheet  of  brown   paper,  draw  a 
circle  around  it,  and  mark  on  the  paper  the  center  of  the  circle, 
i.  e.,  the  position  of  the  center  of  the  compass.      Draw  a  line  east 
and  west  through  this  point  and  mark  off  on  this   line   points  in 
both  directions  at  distances   of   10,    15,    20,    30,   and  40  cm.,  re- 
spectively, from  the  center  of  the  compass.      Remove  all  magnetic 
substances    from    the    neighborhood,    replace    the    compass,   and 
adjust  it  so  that  its  needle  reads  zero  degrees.      (The   compass 
should  be  tapped  very  lightly  as  the  needle  comes  to  rest,  with 
the  finger  or  with  a  rubber  pencil-tip.) 

Hold  a  long  magnetized  steel  strip  in  a  vertical  position  with 
its  lower  end  on  the  table  at  10  cm.  either  east  or  west  of  the 
compass,  and  read  the  deflection  of  the  compass-needle.  (Tap 
the  compass  as  before,  and  read  both  ends  of  the  needle,  averag- 
ing the  readings.)  Repeat  with  the  end  of  the  long  magnet  at 
10  cm.  on  the  other  side  and  average  the  two  deflections  of  the 
compass-needle,  recording  each  observation.  To  what  function 
of  the  angle  of  deflection  is  the  force  exerted  by  the  lower  pole  of 
the  long  magnet  proportional,  assuming  that  the  needle  is  com- 
paratively short  ?  (See  proposition  above.) 

III.  Repeat  the  last  part  of  II  with  the  end  of  the  long  magnet 


27]  LAWS   OF   MAGNETIC   ACTION.  53 

at  15,  20,  30,  and  40  cm.,  respectively,  from  the  center  of  the 
compass,  changing  sides  and  averaging  as  before.  Calculate  from 
your  results  (using  a  table  of  natural  tangents)  the  ratio  of  the 
horizontal  force  due  to  the  lower  pole  of  the  magnet  at  10  cm.  to 
that  at  20  cm. ;  at  15  cm.  to  that  at  30  cm.;  at  20  cm.  to  that  at 
40  cm. ;  etc.  Does  the  force  vary  directly,  or  inversely,  with  the 
distance?  Assuming  that  it  varies  (directly  or  inversely)  as 
some  integral  power  of  the  distance,  what  do  you  find  to  be  the 
power  in  question?  Arrange  results  in  tabular  form. 

IV.  Take  a  comparatively  short  magnet  and  lay  it  on  the  table 
on  a  line  drawn  east  and  west  through  the  center  of  a  compass- 
needle,  at  such  a  distance  as  to  deflect  the  needle  about  40°. 
Read  the  deflection  and  measure  the  distance  from  the  center  of 
the  magnet  to  that  of  the  compass-needle.     Place  the  magnet  at 
double  this  distance,  and  read  the  deflection  again.     Do  you  find 
the  horizontal  force  to  vary  with  the  distance  in  this  case  accord- 
ing to  the  law  found  in  III,  or  not?     Was  the  needle  in  II  and 
III  acted  on  in  a  horizontal  direction  by  both  poles  of  the  magnet, 
or  practically  by  one  alone?     Was  it  in  IV? 

When  a  magnet  is  comparatively  short,  how  do  you  find  the 
force  exerted  by  it  at  any  point  to  vary  with  the  distance  of  the 
point  from  the  center  of  the  magnet,  assuming  that  it  varies  as 
some  exact  integral  power  of  this  distance? 

V.  A  unit  magnetic  pole  is  a  magnetic  pole  of  such  strength 
that  it  will  exert  a  force  of  one  dyne   on  a  similar  pole  at  the  dis- 
tance of  one  cm. 

The  pole  strength  of  a  magnetic  pole  is  defined  as  the  force 
exerted  by  it  on  a  unit  magnetic  pole  at  the  distance  of  one  cm. 

What  is  the  force  between  two  magnetic  poles  at  the 
distance  d  apart,  the  strength  of  the  poles  being  mv,  and  m^ 
respectively  ? 

VI.  If  in  IV  the  magnet  were  in  the  E  and  W  line  and  the 
compass  on  a  line  perpendicular  to  the  middle  point  of  the  mag- 
net, in  the  same  horizontal  plane,  find  geometrically  the  expres- 
sion for  the  force  between  a  compass  pole  and  the  magnet. 


54  MAGNETIC  FIELDS.  [28 

28.     MAGNETIC   FIELDS. 

I.  Take  a  magnet   16.5  cm.   long,   and    locate    approximately 
the  mean  distance  of  either  pole  from  the  end,  by  the  following 
method  :— 

Lay  the  magnet  on  a  sheet  of  paper,  and  trace  its  outline  with 
a  pencil.  Place  a  compass  on  the  paper  so  that  the  compass  box 
is  about  one  cm.  from  the  magnet.  Commencing  near  the  end 
of  the  magnet,  move  the  compass,  one  or  two  cm.  at  a  time, 
parallel  to  the  magnet,  drawing,  for  each  position  of  the  compass, 
lines  to  indicate  the  direction  of  its  needle.  Remove  the  magnet, 
draw  a  line  through  the  position  of  its  axis,  and  extend  the  above 
lines  until  they  intersect  this  line.  Find  a  medium  point  and 
measure  its  distance  from  the  end  of  the  magnet. 

II.  Lay   the   magnet   used   in    I   lengthwise  on   a  large  sheet 
of  brown  paper.      Draw  the  outline  of  the  magnet  with  a  pencil, 
and  sprinkle   iron   filings   on   the   paper  around   it.       Trace  the 
lines  in  which  the  iron  filings  set  themselves  when   the  paper  is 
tapped. 

Brush  the  iron  filings  off  the  magnet,  and  return  them  to  the 
sprinkler,  taking  care  not  to  scatter  and  waste  them.  (In  re- 
moving iron  filings  from  a  magnet,  brush  them  towards  the 
center,  and  not  towards  the  ends.) 

Replace  the  magnet,  and  place  a  small  compass  at  different 
points  of  the  tracing.  How  does  the  direction  of  the  compass- 
needle  at  any  point  coincide  with  that  of  the  lines  of  iron 
filings  ? 

III.  Take   a   sheet  of  cardboard   and  place  it  with    its   sides 
parallel    to   the   edges  of  the   table.      To  the  most   northerly  or 
southerly  corner  of  the  cardboard   fasten  a  small    compass  with 
wax*,   and,    after    removing    all    magnetic   substances   from    the 
neighborhood,     draw    a    pencil    line    to    correspond    with    the 
magnetic    meridian    through  the   compass.       On   this  line  place 

*  Attach  t.ie  wax  to  the  edge  of  the  compass,  and  do  not  put  it  under- 
neath. 


28]  MAGNETIC   FIELDS.  55 

a  short  magnet  with  its  north  pole  directed  toward  the  south, 
and  adjust  the  distance  between  it  and  the  compass  so  that 
the  compass-needle  is  in  neutral  equilibrium  (i.  e.,  will  point 
indifferently  in  any  direction).  Fasten  the  magnet  in  this 
position  to  the  cardboard  with  wax.  The  compass-needle  will 
not  be  affected  now  by  the  earth's  magnetic  field,  while  the 
sides  of  the  cardboard  are  parallel  to  the  edges  of  the  table. 
Why? 

IV.  Take  the  drawing  made  in  II.     Mark  the  position  of  the 
poles  of  the  magnet,    and  draw  a  circle,    about    2   or    3  cm.    in 
diameter,    around  each.     Divide  these  circles  into    12  or  more 
equal  parts,  and  through  each  division  draw  a  line,  following  the 
directions  in  which  the  iron  filings  set  themselves,  as  far  as  these 
directions  can  be  determined. 

Replace  the  magnet  on  the  paper,  and  place  the  compass- 
needle,  protected  as  in  III  from  the  influence  of  the  earth's 
magnetic  field,  at  the  end  of  one  of  these  lines.  Extend  this 
line  an  inch  or  so  in  the  direction  indicated  by  the  needle. 
Prolong  all  the  lines  through  the  divisions  of  the  circle  in  this 
way,  an  inch  or  so  at  a  time,  as  far  as  the  limits  of  the  paper 
will  allow. 

V.  Take  a  point  on  one  of  these  lines  about  9  or  10  cm.  from 
one  of  the  poles  of  the  magnet,  and  12  or  15  cm.  from  the  other 
pole.     Suppose  a  north  or  south  magnetic  pole  to  be  placed  at 
this  point.      Draw  lines  in  the  directions  that  this  pole  would  be 
urged  by  each  pole  of  the  magnet,   and   lay  off  on  these   lines 
distances  proportional  to  the  forces  in  these  directions  due  to  the 
poles  taken  separately.      (Force  varies  inversely  as-  the  square  of 
the  distance. )     Construct  on  these  lines  a  parallelogram  of  forces, 
and  find  the  direction  of  the  resultant  force  due  to  both  poles  of 
the  magnet.     How  does  the  direction  of  this  resultant  compare 
with  that  of  the  magnetic  line  of  force  at  point  considered  ? 

If  it  were  possible  to  produce  an  isolated  north  magnetic  pole 
and  place  it  in  a  magnetic  field,  how  would  the  path  along  which 
it  would  move  be  related  to  the  magnetic  lines  of  force  ?  Deduce 


56  INTENSITY   OF   KARTH's   MAGNETIC   FIELD.  [29 

from  this  a  definition  of  a  magnetic  line  of  force.  How  is  the 
strength  of  the  magnetic  field  due  to  the  magnet  indicated  by  the 
distribution  of  the  lines  of  force  at  any  region  in  the  preceding 
diagram  ? 

The  sheet  of  brown  paper  used  in  II,  IV,  and  V  is  to  be  signed 
and  handed  in  with  the  other  notes.  Each  student,  however, 
should  make  in  his  note-book  a  reduced  copy  of  the  diagram 
before  handing  it  in. 

VI.  Lay  two  short  magnets  on  a  sheet  of  white  paper  with 
impression  paper  and  another  sheet  of  white  paper  underneath 
(or  they  may  be  laid  directly  on  a  page  of  the  note-book).  Lay 
them  parallel,  side  by  side,  about  1.5  or  2  cm.  apart,  with  their 
unlike  poles  opposite.  Sprinkle  iron  filings  about  them,  and 
trace  the  lines  along  which  the  filings  set  themselves. 

29.    INTENSITY   OF    EARTH'S    MAGNETIC    FIELD.     I. 

Caution. — Keep  the  magnet  used  in  this  exercise  away  from 
other  magnets  or  magnetic  bodies. 

I.  (a.)   Place  a  magnet  in  the  east  and  west  line  east  or  west 
of  a  compass-needle,  at  such  a  distance  as  to  deflect  the   needle 
through  an  angle  of  45°.      Measure  the  length  of  the  magnet  and 
the  distance  of  its  nearer  end  from  the  center  of  the  compass. 

(b.)   Reverse  the  magnet  and  repeat  the  measurements  of   (a), 
(c. )   Repeat  (a)  and  (b}  with  the  magnet  on  the  other  side  of 
the  compass-needle. 

II.  (a.)   Suspend  a  carriage  for  the  magnet  by  two  fine  parallel 
wires  of  equal  length,  adjustable  from  above,   so  that  they   are 
east  and  west  of  each  other.      Place  a  brass  rod  of  about  the  same 
size  as  the  magnet  in   the  carriage  and  carefully  draw  a  line  par- 
allel   to    the    rod    on    a    piece    of  paper   placed    underneath    it. 
Remove  the  brass    rod  and    place  the    magnet  in  the  carriage. 
Does    the    magnet  lie,  as  the    rod    did,  east  and   west,  or    not? 
Explain  why.      Mark  on  the  paper  the  position  of  the  magnet. 

(£.)   Reverse  the  magnet  and  mark  its  position  again. 


30]  INTENSITY   OF   EARTH *S   MAGNETIC   FIELD.  57 

(V.)  Measure  the  distance  between  the  two  wires  of  the  bifilar 
suspension,  and  mark  their  position  carefully  on  the  paper  in  the 
three  cases  above.  Find,  by  measurement  from  the  drawing,  the 
average  distance  that  the  lower  end  of  either  wire  is  pulled  out 
from  the  vertical  when  the  magnet  is  hung  in  its  carriage. 

What  forces  cause  the  magnet  to  be  deflected  ?  What  is  the 
direction  of  these  forces,  and  where  do  they  act  on  the  magnet, 
assuming  that  the  poles  of  the  magnet  are  at  its  extremities  ? 
Measure  on  the  paper  the  arm  of  the  couple  (see  Exercise  1 1,  VI) 
formed  by  these  forces. 

Measure  the  length  of  the  bifilar  suspension  and  also  find  the 
weight  of  the  magnet  and  carriage.  Express  these  weights  in 
dynes. 

Repeat  Part  II,  using  another  part  of  the  same  paper. 
Average  the  two  sets  of  results. 

Preserve  the  paper  diagram  for  reference. 

30.    INTENSITY   OF   EARTH'S  MAGNETIC  FIELD.     II. 

This  exercise  need  not  be  performed  in  the  laboratory,  and  is 
to  be  done  only  when  the  other  exercises  on  magnetism  have 
been  performed. 

I.  In  Exercise  29,  I,  how  did  the  horizontal  force  at  the  center 
of  the  compass  due  to  the  magnet  compare  in  each  case  with  that 
due  to  the  earth's  magnetic  field? 

Calculate  the  average  force  on  a  unit  magnetic  pole  at  the 
center  of  the  compass  due  to  the  nearer  pole  of  the  magnet, 
calling  the  pole-strength  of  the  magnet  P  (see  Exercise  27,  V) 
and  assuming  that  its  poles  are  situated  at  its  extremities.  Do 
the  same  for  the  farther  pole  of  the  magnet.  How  did  these 
forces  compare  in  direction?  Find  their  resultant.  How  does 
this  resultant  compare  with  the  horizontal  force  (usually  denoted 
by  the  letter  H)  on  a  unit  magnetic  pole  due  to  the  earth's 
field?  (See  question  above.) 

Form  an  equation  from  these  results  and  find  from  it  the 
numerical  value  of  the  quotient  H/ P. 


5&  COMPARISON    OF   MAGNETIC    FIELDS.  [31 

II.  Assuming   that  the  weight  in  Exercise  29,  II,  was  evenly 
divided  between  the  two  wires  of  the  bifilar  suspension,  calculate 
the  horizontal  force  on  the  lower  end  of  each  wire  tending  to  pull 
it  back  into  a  vertical  position.      Do  this  by  means  of  a  triangle 
of  forces  as  in  Exercise  12,  VI,  using  the  length  of  the  wire  and 
the  deflection  from  the  vertical,  as  measured  in  Exercise  29.      In 
what  direction  did  these  forces  act,  and  what  was  the  arm  of  the 
couple   (see  Exercise   11,  VI)  formed   by  them?     Calculate  the 
moment  of  the  couple  formed  by  these  forces.     Draw  diagrams 
of  forces. 

What  two  forces  tended  to  deflect  the  magnet  ?  To  what  was 
each  of  these  forces  equal  in  terms  of  //and  />?  Calculate  the 
moment  of  the  couple  formed  by  these  forces. 

What  relation  exists  between  the  moments  of  the  two  couples 
just  calculated?  Express  this  relationship  in  the  form  of  an 
equation,  and  calculate  the  numerical  value  of  the  product  //x  P. 

III.  Combine   the  results  found  in  I  and  II  so  as  to  eliminate 
the    unknown    quantity  P  and  .  find    the   value  of  H  in  dynes. 
Calculate  also  the  pole-strength;  in  what  unit  is  it  expressed? 

IV.  Write  not  less  than  two  hundred   words  on  the  subject: 
Terrestrial  Magnetism. 

31.    COMPARISON    OF    MAGNETIC    FIELDS. 

I.  Suspend  a  magnet  in  a  horizontal  position  by  a  long  thread 
(a  torsionless  thread,  if  possible),  and  protect  it  from  air  currents 
by  hanging  it  in  a  box.  When  the  suspended  magnet  has  been 
brought  to  rest,  set  it  vibrating  about  a  vertical  axis  by  bringing 
an  open  knife  blade  near  it,  and  determine  its  period  of  vibration 
within  a  few  hundredths  of  a  second.*  Be  careful  not  to  touch 
the  magnet  with  magnetic  substances,  and  also  keep  all  movable 
magnetic  bodies  away  from  the  neighborhood  of  the  vibrating 
magnet. 


Find  the  period  by  the  method  of  Exercise  15. 


32]  ELECTRO-MAGNETIC   RELATIONS.  59 

II.  Mark  in  some  way  the  position  of  one  end  of  the  magnet, 
remove  it,  and  place  a  compass  with  a  short  needle  at  this  point. 
Place  a  long  magnet  at  right  angles  to  a  line  drawn  east  and  west 
through  the  thread  with  its  center  on  this  line  and  its  south  pole 
towards  the  south.     Move  this  magnet  parallel  to  itself  until  the 
earth's  horizontal  field  at  the  center  of  the  compass  is  as  nearly 
neutralized   as  possible.     Then  turn  the  magnet  through  180°, 
i.  e.,  end  for  end.     Will  the  intensity  of  the  horizontal  magnetic 
field   at    the  compass-needle   now    be   greater    or  less  than    the 
earth's  horizontal  field,  //?     How  much  greater  or  less? 

Remove  the  compass,  replace  the  suspended  magnet,  and 
determine  its  period  of  vibration  again  as  in  I.  Calculate  the 
ratio  of  the  periods  in  the  two  cases.  How  does  this  compare 
with  the  intensity  of  the  horizontal  magnetic  fields  in  the  two 
cases? 

Assuming  that  the  period  of  a  vibrating  magnet  varies  as 
some  integral  root,  or  power,  of  the  intensity  of  the  magnetic 
field  parallel  to  the  magnet,  what  do  your  results  indicate  this 
root,  or  power,  to  be?  Is  it  direct  or  inverse? 

III.  Suspend    your  magnet   at  two  designated  places  in    the 
aboratory,  determining  its  period  of  vibration  at  each  place  and 
also  at  a  place  where  //is  known.     From   your  results  and  the 
law  just  found,   calculate  the  value  of  H  at  each  of  the  places 
where  the  magnet  was  vibrated. 

IV.  If  the  suspending  string  were  not  torsionless,  would  the 
calculated  values  of  H  be  too  high  or  too  low  ?     Explain. 

What  analogies  exist  between  this  magnetic  pendulum  and  the 
simple  gravity  pendulum  ? 

32.     ELECTRO-MAGNETIC    RELATIONS. 

I.  Connect  the  plates  of  a  Daniell  cell  by  a  flexible  wire  cord. 
Stretch  a  portion  of  this  cord  out  straight  and  hold  it  near  a 
compass-needle  placed  on  the  edge  of  a  wooden  block.  The 
electric  current  is  supposed  to  flow  through  the  external  circuit 


60  ELECTRO-MAGNETIC  RELATIONS.  [32 

from  the  copper  plate  of  the  cell  to  the  zinc  plate.  In  what 
direction  is  the  north  pole  of  the  compass-needle  deflected,  or  is 
it  deflected  at  all,  when  the  current  and  the  needle  are  in  the 
following  relative  positions:— 

1.  Current  flowing  north,  needle  below? 

2.  Current  flowing  north,  needle  above  ? 

3.  Current  flowing  north,  needle  east  or  west? 

4.  Current  flowing  south,  needle  below  ? 

5.  Current  flowing  south,  needle  above? 

6.  Current  flowing  south,  needle  east  or  west? 

7.  Current  flowing  upward,  needle  north? 

8.  Current  flowing  upward,  needle  south? 

9.  Current  flowing  downward,  needle  north  ? 

10.  Current  flowing  downward,  needle  south? 

1 1 .  Current  flowing  east  or  west,  needle  above  or  below  ? 

12.  Current  flowing  east  or  west,  needle  north  or  south? 

II.   Answer  the  following  questions: — 

1.  How  is   the  direction   in  which  the  compass-needle   is  de- 
flected affected  by  reversing  the  direction  of  the  current? 

2.  How  is  it  affected  when  its  position  is  changed  from  one 
side  of  the  current  to  the  other,  i.  e.,  from  above  to  below  and 
from  east  to  west  ? 

3.  Is  the  force  exerted  by  an  electric  current  on  a  magnetic 
pole  parallel  to  the  direction  of  the  current  or  not  ?     What  do  the 
results  of  I,  i  and  2,  indicate? 

4.  What  is  the  direction  of  this  force,  with  reference  to  the 
plane  containing  the  current  and  the  magnetic  pole,  as  indicated 
by  the  results  of  I,  3  and  6  ? 

5.  If  the  needle  was  not  deflected  in  I,  n,  explain  why. 

6.  Suppose  the  current  is  represented  in  position  and  direction 
by  the  fingers  of  the  right  hand    and    the    palm    to   be    turned 
towards    the  compass-needle,    which    pole  was   deflected   in    the 
direction  indicated    by  the  thumb  in  I,  i;  in  I,  2;  in  I,  3,  etc.? 
Frame  a  rule  including  all  the  above  cases. 


32]  ELECTRO-MAGNETIC   RELATIONS.  6l 

III.  Connect  the  plates  of  the  Daniell  cell  to  a  rectangular  coil 
suspended  with  its  terminals  in  mercury  cups  so  as  to  turn  freely 
about  a  vertical  axis.      Set  the  coil  with  its  plane  north  and  south. 
Follow  the  path  of  the  electric  current  from  the  copper  plate  of 
the  cell  through  the  coil  to  the  zinc  plate,  and  find  in  what  part 
of  the  coil  the  current  flows  in  a  northerly  direction,  in  what  in  a 
southerly    direction,    in    what    part    upward,    and    in    what    part 
downward. 

Take  a  magnet  and  hold  its  north  pole  in  the  following 
positions  relative  to  the  current,  observing  in  each  case  the 
direction  in  which  the  wire  carrying  the  current  tends  to 
move: — 

1.  Current  flowing  north,  north  pole  below. 

2.  Current  flowing  north,  north  pole  above. 

3.  Current  flowing  south,  north  pole  below. 

4.  Current  flowing  south,  north  pole  above. 

5.  Current  flowing  upward,  north  pole  north. 

6.  Current  flowing  upward,  north  pole  south. 

7.  Current  flowing  downward,  north  pole  north. 

8.  Current  flowing  downward,  north  pole  south. 

How  does  the  force  exerted  by  a  magnetic  pole  upon  an  electric 
current  compare  in  direction  with  that  exerted  by  the  current 
upon  the  pole?  (Compare  the  results  of  I  and  III.) 

IV.  Trace  by  means  of  iron  filings  the  magnetic  field  due  to  a 
helical  coil  carrying  a  current.     To  the  field  of  what  shape  mag- 
net does  this  resemble  ? 

Test  the  coil  with  a  compass-needle  and  determine  which  end 
attracts  the  north  pole  and  which  the  south  pole  of  the  needle. 
Could  the  position  of  its  poles  be  determined  beforehand?  How  ? 

V.  What  do  you  conclude  from  I,  II,  and  III  to  be  the  form 
of  the  magnetic  field  about  a  wire  carrying  a  current? 

How  does  an  electric  circuit  tend  to  set  itself  with  respect  to 
the  number  and  direction  of  the  magnetic  lines  of  force  in  its 
neighborhood?  (A  magnetic  line  of  force  proceeds  from  the 
north  pole  to  the  south  pole  outside  the  magnet.) 


62  LAWS   OF   ELECTROMAGNETIC    ACTION.  [33 

Does  the  coil  used  in  III  act  as  if  it  were  itself  a  magnet?     If 
so,  of  what  form  ? 


33.     LAWS   OF    ELECTRO-MAGNETIC  ACTION. 

I.  Take  an  upright  wooden  circle  about  30  cm.   in  diameter, 
having  apiece  of  insulated    copper  wire  wound  once  around  it, 
with  two  free  ends  of  about  equal  length  twisted  together  so  that 
the  effect  of  an  electric  current  in  one  will  be  neutralized  by  that 
of  an  equal  and  opposite  current  in  the  other.    •  Place  a  compass- 
needle  at  the  center  of  the  coil,  and  set  the  coil  so  that  its  plane 
is  parallel  to  the  magnetic  meridian. 

Connect  this  galvanometer  with  some  source  furnishing  a 
constant  electric  current.  Read  the  angle  of  deflection  of  the 
compass-needle.  Reverse  the  direction  of  the  current  and  read 
the  angle  again.  Average  the  two  results. 

In  what  direction  is  the  force  tending  to  deflect  the  needle? 
(See  Exercise  32.)  To  what  function  of  the  angle  of  deflection 
is  this  force  proportional?  (See  Exercise  27,  Proposition.) 

II.  Repeat  I  with  a  coil  of  the  same    diameter,   but    having 
twice  the  length  of  wire  as  in  I,  i.  e.,  having  twice  as  many  turns 
of  wire. 

III.  Take  another  wire  and  wind   it  once   around  a  wooden 
circle  concentric  with  and  of  half  the  diameter  of  that  used  in  I. 
Connect  these  two  coils  so  that  the  same  current  will  flow  through 
them  in  opposite  directions.     Increase  the  number  of  turns  of  the 
larger  coil  until  the  effect  of  the    smaller  coil  on  the  compass- 
needle  is  neutralized.      How  many  turns  of  wire  were  necessary 
to  do  this  ?     How  many  times  did  the  length  of  the  wire  have  to 
be  increased  from  that  of  the  single  turn  on  the  inner  coil  in  order 
to  neutralize  the  effect  due  to  the  decrease  in  the  diameter  of  the 
coil? 

IV.  Set  up  three  such  galvanometers  having  coils  of  the  same 
diameter  and  length,  placing  them  as  far  apart  as  the  table  will 
allow,  and  connect  them  so  that  the  whole  current  passes  through 


33]  LAWS  OF   ELECTRO-MAGNETIC   ACTION.  63 

one  coil  and  half  of  the  current  through  each  of  the  other  coils. 
Read  the  angle  of  deflection  of  each  compass-needle.  Reverse 
the  direction  of  the  current  and  average  the  east  and  west  deflec- 
tions of  each  galvanometer. 

V.  Answer  the  following  questions,  showing  in  each  case  the 
numerical  process  by  which  you  arrived  at  your  conclusion: — 

1.  How  does  the  force  at  the  center  of  a  circular  coil  carry- 
ing an  electric  current  vary  with  the  length  of  wire  in  the   coil, 
according  to  the  results  of  I  and  II,  assuming  that  it  varies  with 
some  integral  power  (direct  or  inverse)  of  the  length  ? 

2.  How  with  the  diameter  or  radius  of  the  coil,  according  to 
the  results  of  II  and  III? 

3.  How  with  the  current,  according  to  the  results  of  IV? 
Assuming  that  the  force  F  on  a  unit    magnetic  pole   at  the 

center  of  a  circular  coil  depends  only  on  the  length,  L=2.nRN, 
of  wire  in  the  coil,  its  radius,  R,  and  the  current,  C,  express  this 
force  in  terms  of  these  three  quantities  and  a  constant  K. 

VI.  Draw  diagrams  of  all  electrical  connections. 
Represent  graphically  the  magnetic  field  at  the  needle  when  the 

latter  is  deflected  45°. 

GROUP   IV. 

In  all  the  electrical  experiments,  diagrams  of  electrical  connec- 
tions are  to  be  made. 

Instruments  of  the  tangent  galvanometer  type— a  loop  of  wire 
about  a  magnetized  needle — should  be  set  with  the  plane  of  the 
coil  in  the  magnetic  meridian  and  leveled  so  that  the  needle 
swings  freely.  Wires  leading  to  such  an  instrument,  or  near  it, 
should  be  twisted  or  laid  side  by  side  so  that  the  magnetic  fields 
of  currents  in  opposite  directions  neutralize  each  other.  Two 
instruments  should  never  be  nearer  each  other  than  one  metre. 

To  take  an  observation,  read  both  ends  of  the  pointer,  reverse 
the  direction  of  the  current,  read  both  ends  of  the  pointer  again, 
and  average  the  four  readings.  Reading  both  ends  of  the 


64  CURRENT    DETERMINATION.  [34 

pointer  eliminates  eccentricity  of  mounting  of  the  needle  with 
respect  to  the  scale.  Reversing  the  current  corrects  for  the 
imperfect  orientation  of  the  coil  in  the  magnetic  meridian.  Note 
that  the  pointer  is  usually  mounted  at  right  angles  to  the  needle. 
In  the  case  of  needles  mounted  on  pivots  slight  tapping  of  the 
instrument  may  be  necessary  to  insure  a  correct  reading.  The 
influence  of  one  instrument  upon  "another  may  be  tested  by 
reversing  the  current  through  one  of  them. 

It  is  important  in  all  electrical  work  that  the  connections  be 
tight.  Always  disconnect  from  batteries  when  through. 

In  all  cases  the  above  methods  are  to  be  used  and  the  indicated 
precautions  taken. 

34.   CURRENT   DETERMINATION. 

I.  Connect   a    tangent   galvanometer,   such    as    was    used    in 
Exercise  33,  in  series  with  an  ammeter  and  a  source  of  constant 
current,  following    the    preceding    directions   for  setting  up  and 
reading.      Take  five   sets  of  readings  on  different  parts    of  the 
scale  of  both  instruments  simultaneously,  varying  the  current  by 
introducing    into    the    circuit    various    lengths   of  German  silver 
wire.      Record  all  readings  and  take  the  proper  averages. 

II.  From    the    laws    of    electro-magnetic    action    studied    in 
Exercise  33  we  may  calculate  the  value  of  the    current  for  the 
various  readings  of  the  galvanometer,  and  comparing  these  values 
with  the  ammeter  readings,  both  expressed  in  the  same  unit,  we 
may  calibrate  or  test  the  ammeter. 

The  C.  G.  S.  unit  of  current  in  the  electro-magnetic  system  is 
the  current  that  will  act  with  a  force  of  one  dyne  on  a  unit  mag- 
netic pole  at  the  center  of  an  arc  i  cm.  long  of  i  cm.  radius. 
If  C  in  the  equation  of  Exercise  33,  V,  was  measured  in  terms  of 
this  unit,  F  in  dynes,  and  R  and  L  in  cm.,  the  constant  K  may 
be  eliminated.  How?  Solve  the  resulting  equation  for  C. 

Also  F=H  tan  6  where  H  is  the  horizontal  component  of  the 
earth's  magnetic  field  and  0  the  angle  of  deflection  of  the  needle. 


35]  ELECTRICAL    RESISTANCE.  65 

Now  F  is  the  same  quantity  in  the  above  two  equations.  The 
two  values  of  F  may  therefore  be  equated  and  an  expression  for 
the  current  through  the  galvanometer  found  in  C.  G.  S.  units  in 
terms  of  the  four  measurable  quantities:  the  radius  R  of  the  coil, 
the  length  L=27rRN  of  wire  in  fhe  coil  (where  N  is  the 
number  of  turn,s),  the  horizontal  component  H  of  the  earth's 
field,  and  the  tangent  of  the  angle  of  deflection  6.  (The  value 
of  H  will  be  given.) 

III.  Measure  the  radius  of  the  galvanometer  coil  and  find  its 
length.      Calculate  the  values  of  the  current,  in  C.  G.  S.  units,  for 
the  readings  of  the  galvanometer  taken  in  I. 

How  do  the  calculated  values  agree  with  the  ammeter  readings 
of  the  current  ?  What,  then,  is  the  ratio  between  the  C.  G.  S. 
unit  of  current  and  the  ampere — the  practical  unit  indicated  by 
the  ammeter? 

IV.  Make  a  table  of  corrections  to  the  readings  of  the  ammeter 
in  terms  of  the  current  as  calculated. 

V.  Explain    what  reversing  the  current  in  a  tangent  galvano- 
meter eliminates? 

35.    ELECTRICAL   RESISTANCE. 

I.  (a.)  Connect  an  ammeter  directly  with  the  battery  terminals 
and  read  the  current.  Disconnect  as  soon  as  possible. 

(£. )  Introduce  50  cm.  of  No.  25  German  silver  wire  into  the 
circuit  in  series  with  the  ammeter.  Read  the  current.  How  was 
its  value  altered,  by  introducing  this  wire  into  the  circuit? 

(c.)  Repeat  with  100  cm.  of  No.  25  German  silver  wire,  at 
the  same  time  introducing  into  the  circuit  a  wire  equal  in  size  and 
length  to  the  wires  leading  to  the  battery.  What  is  the  effect  on 
the  current  of  doubling  the  length  of  the  wire  in  the  circuit? 

If  we  consider  that  the  wire  offers  resistance  to  an  electric 
current,  and  assume  that  the  resistance  varies  as  some  integral 
power  of  its  length,  what  do  the  results  of  ($)  and  (<:)  show  this 
power  to  be  ?  Is  it  direct,  or  inverse  ? 


66  ELECTRICAL   RESISTANCE.  [35 

II.  (a.)   Repeat  I  (<:)   with   two  No.  25    German  silver  wires, 
each    100  cm.  long,  connected  in  parallel,  instead  of  the  single 
wire.      What    is    the    effect    upon  the  current  of  paralleling  the 
resistance    wire    with  another  wire  of  the  same  material  and  of 
equal  diameter  and  length  ?  • 

(£.)  Remove  the  extra  wire  inserted  in  the  circuit  in  i  (V),  and 
adjust  the  length  of  the  two  wires,  so  that  the  current  through 
the  ammeter  is  the  same  as  in  I  (£).  How  does  the  resistance  of 
the  two  wires  in  parallel,  after  this  adjustment,  compare  with  the 
resistance  of  the  single  wire  in  I  (b)  ?  How  do  their  lengths 
compare?  What  do  you  find  to  be  the  ratio  of  the  resistance  of 
a  single  wire  to  that  of  two  wires  of  the  same  material,  length,  and 
diameter  connected  in  parallel? 

III.  (0.)   Connect  a  No.  25  German  silver  wire  20  cm.  long  in 
series  with  the  ammeter  and  read  the  current. 

(£.)  Replace  the  No.  25  German  silver  wire  by  a  No.  20 
German  silver  wire  of  the  same  length,  and  measure  the  current 
again.  What  do  you  find  to  be  the  effect  of  increasing  the  cross- 
section  of  a  wire  upon  the  current  ? 

(V.)  Adjust  the  length  of  the  No.  20  German  silver  wire  so  that 
the  current  through  the  ammeter  is  the  same  as  in  III  (a).  How 
does  the  length  of  the  No.  20  wire  compare  with  that  of  a  No. 
25  wire  having  the  same  electrical  resistance  ? 

(d.)  With  a  screw  gauge  meaure  the  diameter  of  the  No.  25 
and  also  of  the  No.  20  wire.  What  is  the  ratio  of  the  diameters 
of  the  two  wires?  What  is  the  ratio  of  the  resistance  of  a  No. 
25  wire  to  that  of  the  same  length  of  No.  20  wire  ?  Explain. 
Assuming  that  the  electrical  resistance  varies  as  some  integral 
power  of  the  diameter  of  a  wire,  what  do  you  find  the  power  in 
question  to  be  ?  Is  it  direct,  or  inverse  ?  How  must  the  resist- 
ance vary,  then,  with  the  cross-section  of  the  wire  ?  How  do  the 
results  of  II  (£)  confirm  your  answer  to  this  last  question  ? 

IV.  (a.)   Introduce  50  cm.  of  No.  25  nickel  wire  into  the  cir- 
cuit, instead  of  the  German  silver  wire,  and  measure  the  current. 


36]  ELECTROMOTIVE    FORCE.  67 

What  is  the  ratio  of  the  resistance  of  the  German  silver  and  nickel 
wires  of  the  same  length  and  diameter? 

(£.)  Replace  the  brass  wire  by  the  No.  20  German  silver 
wire  and  adjust  its  length  so  that  the  current  through  the 
ammeter  is  the  same  as  in  IV  (a). 

Having  found  a  certain  length  of  No.  20  German  silver  wire 
equal  in  resistance  to  50  cm.  of  No.  25  nickel  wire,  and  knowing 
the  diameters  of  these  wires,  calculate  the  relative  resistance  of 
nickel  and  German  silver  wires  of  the  same  diameter  and  length. 

V.  The  resistance  of  a  cubic  centimeter  is  called  the  specific 
resistance  of  a  substance.  If  the  specific  resistance  of  German 
silver  is  known,  show  how  that  for  nickel  may  be  calculated  from 
your  results.  Write  the  equation  representing  this. 

36.    ELECTROMOTIVE   FORCE. 

I.  (a. )  Connect  a  low-resistance  galvanometer  (an  ammeter) 
directly  to  a  Daniell  cell  and  note  the  reading.  Introduce 
another  Daniell  cell  into  the  circuit  in  series  with  the  first  cell, 
connecting  the  copper  plate  of  one  cell  to  the  zinc  plate  of  the 
other,  so  that  the  currents  due  to  both  flow  in  the  same  direction 
through  the  ammeter.  What  change  did  the  second  cell  produce 
in  the  reading  of  the  ammeter,  if  any  ? 

(£.)  Repeat  (a)  with  a  high-resistance  galvanometer,  con- 
structed so  that  the  effect  on  the  deflection  due  to  diminishing  the 
current  is  offset  by  having  a  great  number  of  turns  in  the  coil. 
How  did  the  change  in  the  reading  produced  by  introducing  an 
additional  cell  into  the  circuit  compare  with  that  produced  by  the 
additional  cell  when  an  ammeter  was  used  ?  Should  a  galva- 
nometer of  high  or  low  resistance  be  used  to  show  the  effect  of 
connecting  two  battery  cells  in  series? 

The  effect  of  connecting  two  cells  in  series  is  to  double  the 
electromotive  force*  tending  to  produce  an  electric  current  in 


*The  practical  unit  of  electromotive  force  is  called  a  volt,  and  a  high- 
resistance    galvanometer  graduated    to  give  the   electromotive    force 


68  ELECTROMOTIVE    FORCE.  [36 

the  circuit.  What  sort  of  a  galvanometer  (high  or  low  resistance) 
do  your  results  indicate  should  be  used  to  measure  the  electro- 
motive force  due  to  any  source  of  electric  currents,  or  between  two 
points  of  a  circuit  carrying  a  current  ?  What  is  the  objection  to 
using  a  high-resistance  galvanometer  to  measure  the  current  in  a 
circuit? 

II.  With  a  voltmeter  measure  the  electromotive  force  of  the 
following  cells  and  combinations  of  cells,  anal  answer  the  questions 
asked.      (The  directions  for  using  a  galvanometer  apply  also  to  a 
voltmeter.) 

1.  A  Daniell  cell. 

2.  Two  Daniell  cells  in  series,  connected  copper  to  zinc. 

3.  Two  Daniell  cells  in  series,  connected  copper  to  copper. 

4.  Two  Daniell  cells  in  parallel. 

Are  the  electromotive  forces  of  the  individual  Daniell  cells 
equal?  (Compare  i,  2,  and  3.)  How  does  the  electromotive 
force  of  two  Daniell  cells  in  parallel  compare  with  that  of  a  single 
cell?  With  that  of  two  cells  in  series?  (Compare  1,2,  and  4.) 

5.  A  Leclanche  cell.      (Zinc  and  carbon  plates  in  a  solution  of 
sal  ammoniac, — ammonium  chloride.) 

6.  A  Leclanche  and  a  Daniell  cell  in  series,  connected  carbon 
to  zinc  and  copper  to  zinc. 

7.  The  same  cells  in  series,  connected  carbon   to   copper  and 
zinc  to  zinc. 

Is  the  electromotive  force  of  a  battery  cell  altered  in  any  way 
when  it  is  connected  to  another  cell  of  different  construction  ? 
(Compare  1,5,  6,  and  7.) 

8.  Any  other  cells  or  sources  of  electromotive  force  provided. 

III.  Measure  the  electromotive  force  of  a  Daniell  cell,  and  of  a 
Leclanche  cell,  after  being  short-circuited  for  fifteen  or   twenty 
minutes.     Was    the  electromotive  force    of  the  Daniell  cell   the 


between  its  terminals  in  volts  is  called  a  vo'tmeter.  The  instruments  of 
this  class  used  in  (b)  were  designed  for  use  as  voltmeters  and  will  be 
designated  as  such  hereafter.  The  electromotive  force  of  a  Daniell  cell 
is  1.07  volt. 


37]  OHM'S  LAW.  69 

same  as  that  found  in  II?  Was  that  of  Leclanche  the  same?  If 
not,  why?  Which  cell  do  you  conclude  is  unsuitable  for  use 
where  a  constant  current  is  required,  as  in  telegraphing  ?  Give  a 
reason  why  the  other  cell  would  be  unsuitable  for  use  where  the 
circuit  would  only  be  closed  for  a  moment  at  a  time  and  at  long 
intervals,  as  on  a  bell  circuit.  Disconnect  all  wires  from  cells. 
Is  electromotive  force  a  force?  Explain. 


37.     OHM'S    LAW. 

I.  («.)  Connect  a  single  Daniell  cell  in  series  with  a  rheostat 
and  an  ammeter.  Take  out  enough  plugs  from  the  rheostat  to 
introduce  a  resistance  of  5  ohms*  into  the  circuit.  Read  the 
ammeter  carefully,  reversing  as  usual.  (Do  not  be  surprised  if 
the  current  is  small.) 

(3.)  Introduce  another  Daniell  cell  into  the  circuit  in  series  with 
the  first  cell.  Read  the  ammeter  again. 

(The  electromotive  force  in.  (6)  is  twice  that  in  (a).  (See 
Exercise  36,  II.)  What  relation  do  you  find  to  exist  between 
the  electromotive  force  and  the  current  when  the  resistance  is 
constant  ? 

II..  (a.)  With  the  connections  as  in  I  (£)  take  out  enough 
plugs  from  the  rheostat  to  increase  the  introduced  resistance  to  7 
ohms.  Read  the  ammeter. 

(<£.)  Repeat  II  («)  with  all  the  rheostat  plugs  out.  (Resist- 
ance=io  ohms.) 

How  do  the  currents  through  the  ammeter  in  I  (£),  II  (a), 
and  II  ($),  compare?  How  do  the  resistances  of  the  circuits 
compare,  neglecting  the  comparatively  small  resistance  of  the 
battery  cells  ?  What  relation  do  you  find  to  exist  between  the 
resistance  and  the  current  when  the  electromotive  force  is 
constant  ? 


*The  ohm  is  equal  t«»  the  resistance  at  o°  C.  of  a  column  of  mercury 
106.3  cm.  long  and  i  sq.  mm.  in  cross  section. 


7O  DIVIDED   CIRCUITS.  [38 

What,  from  the  results  of  I  and  II,  is  the  relation  between 
the  current  in  a  circuit  (or  part  of  a  circuit),  the  electromotive 
force  acting  through  the  circuit  (or  between  its  terminals,  if  it  is 
not  a  complete  circuit),  and  the  resistance  of  the  circuit  (or  part 
of  a  circuit)?  This  relation,  when  written  correctly  in  the  form 
of  an  equation  (assuming  the  units  of  current,  electromotive  force, 
and  resistance  to  be  so  related  that  the  constant  factor  is  unity), 
is  called  Ohm' s  Law. 

III.  Connect  the  ammeter  in  series  with  a  rheostat  and  two 
Daniell  cells  in  parallel.  Vary  the  resistance  by  steps  of  one 
ohm  over  the  range  of  the  rheostat.  Read  the  corresponding 
currents.  Make  a  plot  with  values  of  resistance  as  abscissae  and 
products  of  current  by  resistance  as  ordinates.  Also  plot  resist- 
ances and  currents  on  the  same  paper.  Explain  by  Ohm's  law 
the  forms  of  the  lines  drawn. 

Show  how  the  resistance  varies  with  the  electromotive  force 
when  the  current  is  constant. 

38.     DIVIDED   CIRCUITS  AND  FALL  OF  POTENTIAL 
ALONG  A  CONDUCTOR. 

I.  (a.)  Join  two  rheostats  in  parallel  and  connect  them  in 
series  with  the  battery  provided  and  an  ammeter.  Cut  out  the 
resistances  in  the  rheostats,  leaving  but  one  ohm  in  one  branch  of 
the  circuit,  and  two  ohms  in  the  other.  Read  the  current  through 
the  ammeter. 

(£.)  Place  the  ammeter  in  the  branch  circuit  of  one  ohm's 
resistance,  and  measure  the  current  in  this  branch. 

(<:.)  Measure  in  the  same  way  the  current  in  the  branch  circuit 
of  two  ohms'  resistance. 

(d.^)  Answer  the  following  questions: — 

1.  How  does  the  current  in  the  main  circuit  compare  with  the 
sum  of  the  currents  in  the  two  branch  circuits? 

2.  Does  the  greater  current  flow  through  the  circuit  of  greater 
or  less  resistance? 


38]  DIVIDED   CIRCUITS.  71 

3.  The  currents  in  a  divided  circuit  are  proportional  to  an 
integral  power  of  the  resistances  of  the  branches.  What  do  your 
results  indicate  this  power  to  be?  Is  it  direct,  or  inverse? 

II.  Connect  the  two  rheostats  with  a  third  so  as  to  form  'three 
parallel  circuits  of  one,  two,  and  three  ohms'  resistance,  respect- 
ively.      Measure  with  an  ammeter,  as  was  done  in  I,  the  current 
in  the  main  circuit  and  in  each  of  the  branch  circuits.     Measure 
with  a  voltmeter  the  electromotive  force  between  the  two  junctions 
of  the  parallel  circuits. 

Is  the  relation  found  in  I  between  the  currents  in  the 
branch  circuits  and  the  resistances  of  the  circuits  confirmed  by  the 
results  of  II  ?  Explain. 

III.  Connect  an  external  resistance  of  10  ohms  having  steps  of 
2  ohms,  in  series  with  the  battery. 

Connect  one  of  the  voltmeter  terminals  to  one  plate  of  the 
battery  and  the  other  terminal  to  points  on  the  rheostat  separated 
from  this  plate  by  resistances  of  2,  4,  6,  8,  10  ohms,  respectively. 
Plot  resistances  as  abscissae  and  voltmeter  readings  as  ordinates. 
What  does  the  plot  indicate  to  be  the  relation  between  the  fall  of 
potential  along  a  conductor  and  the  corresponding  resistances  ? 
Is  the  fall  of  potential  over  2  ohms'  resistance  the  same  in  all  parts 
of  the  circuit? 

IV.  Calculate  from  the  readings  of  the  ammeter  and  voltmeter, 
by  means  of  Ohm's  law,*  the  combined  resistance  of  the  three 
circuits  in  II  when  joined  in  parallel. 

What  relation  exists  between  this  resistance  and  the  resistances 
of  the  separate  branches? 

The  reciprocal  of  the  resistance  of  a  conductor  of  electricity  is 
called  its  conductivity.  Calculate  the  conductivity  of  each  of  the 
parallel  circuits  in  II  separately,  and  also  the  conductivity  of  the 
three  in  parallel.  What  relation  exists  between  the  conductivity* 
of  the  whole,  and  the  sum  of  the  conductivities  of  the  separate 
branches,  of  the  circuit  ? 


For  statement  of  Ohm's  law,  see  text-book  or  Exercise  37. 


72  ARRANGEMENT   OF    BATTERY    CELLS.  [39 

V.  Deduce  algebraically  from  Ohm's  law  the  relations  found 
experimentally  in  I  and  II,  finding  the  equations  for  the  resistance 
of  circuits  of  two  and  of  three  branches  in  parallel. 


39.    ARRANGEMENT    OF    BATTERY     CELLS;    THEIR 

ELECTROMOTIVE    FORCE  AND    INTERNAL 

RESISTANCE. 

I.  Connect  three  Daniell  cells  in  series  with  each  other  (zinc  to 
copper)  and  in    series  with  an    ammeter  and  a    rheostat.     Also 
connect  a  voltmeter  to  the  terminals  of  the  battery.      Read  the 
voltmeter   and    ammeter    simultaneously,   varying    the    external 
resistance  from  o  by  steps  to  the  limit  of  the  rheostat.      Discon- 
nect the  ammeter  and  rheostat  and  read  the  voltmeter. 

II.  Repeat  I  with  the  three  cells  in  parallel  (coppers  together 
and  zincs  together). 

III.  What  from  I  and  from  II  is  the  value  of  the  electromotive 
force    of  a  single   Daniell  cell?     Measure  this    quantity  directly 
with  the  voltmeter.      Also  read  the  ammeter  connected  to  a  single 
Daniell  cell. 

By  Ohm's  Law  find  the  internal  resistance  of  a  single  Daniell 
cell,  of  three  in  parallel  and  of  three  in  series.  What  are  the 
corresponding  electromotive  forces  ? 

IV.  Construct    a  plot,    from    the  results  of  II,   with  external 
resistances   (R)   as  abscissae    and  terminal  potential  differences 
(E'=CR   where  C=current)   as  ordinates.      The    electromotive 
force  E  of  the  battery  is  given  by  the  voltmeter  reading  on  open 
circuit.      Indicate  this  quantity  on  the  plot  also.      For  what  resist- 
ance in  the  external  circuit  does  the  terminal  potential   difference 
become    zero  ?     On  what  does  the  terminal  potential  difference 
depend?     Deduce  an  equation  (based  on  Ohm's  law)  giving  the 
relation  between  the  electromotive  force  of  a  battery  in  terms  of 
the    internal  and  external  resistances  and  the  current.     Modify 
this  to  include  the  terminal  potential  difference. 


40]  COMPARISON   OF   RESISTANCES.  73 

V.  In  I  and  II,  which  arrangement  of  cells  gave  the  greatest 
current  when  there  was  no  external  resistance  in  the  circuit? 
Which  when  the  highest  resistance  used  was  introduced?  Ex- 
plain why  in  each  case. 

In  general,  how  should  a  number  of  cells  be  connected  in  order 
to  obtain  the  greatest  possible  current  ? 

(i.)  When  the  resistance  in  the  external  circuit  is  very  small. 

(2.)   When  comparatively  large. 

Explain  these  results  algebraically  by  Ohm's  law. 

40.    COMPARISON    OF     RESISTANCES    BY     WHEAT- 
STONE'S   BRIDGE. 

I.  Connect  a  Leclauche  cell  to  the  bridge-wire  of  a  Wheat- 
stone's    bridge,  and  connect    a    sensitive    galvanoscope,   by    one 
terminal,  to  the  sliding  contact.      (As  the  galvanoscope  is  simply 
used  to  show  the  presence  or  absence  of  an  electric  current,  the 
motion  of  its  needle  is  restricted  to  a  few  degrees.)     Connect  also 
two  rheostats  in  series  with  each  other  and  in  parallel    with  the 
bridge-wire,  and  join  the  free  terminal  of  the  galvanoscope  to   the 
junction   of  the  two  rheostats.      A  circuit  of  six  branches  is  thus 
formed,  with  the  galvanoscope  in  one  branch,  the  battery  cell  in 
another,  the  rheostats  in  two  branches,  and  two  branches  formed 
by  portions  of  the  bridge-wire. 

With  a  resistance  of  five  ohms  in  each  rheostat  set  the  sliding 
contact  so  that  there  is  no  current  through  the  galvanoscope. 
Interchange  the  rheostats  and  repeat. 

Measure  the  lengths  of  the  two  portions  into  which  the  bridge- 
wire  is  divided  in  each  case.  What  is  the  mean  ratio  of  these 
two  lengths?  How  does  this  ratio  compare  with  the  ratio  between 
the  two  resistances  in  the  rheostats  ? 

II.  Repeat  I,  with  resistances  of  5  and  10  ohms,  respectively, 
in    the    rheostats;  with  resistances  of    7    and    10   ohms.     What 
proportion  do  you  find  can  always  be  formed  between  the  resist- 
ances  in  the  rheostat  branches  and  the  two  lengths  into  which 


74  HEATING   EFFECT   OF  AN   ELECTRIC   CURRENT.  [41 

the  bridge-wire  is  divided  when  there  is  no  current  through  the 
galvanoscope  ?     Indicate  clearly. 

III.  What  must  be  the  difference  of  potential  between  the  two 
points    where  the  galvanoscope  is    connected  when  there    is  no 
current    indicated?     Why?    Show,   by    applying   Ohm's  law    to 
the    four  branches  formed  by  the    two  parts  of  the  bridge-wire 
and  the  two  resistances,  that,  when  this  is  the  case,  the  proportion 
found  in  II  must  hold  true. 

IV.  Replace  one  of  the  rheostats  by  100  cm.  of  No.  25  German 
silver  wire.     Adjust  the  sliding  contact  so  that  there  is  no  current 
through  the  galvanoscope,  and  measure  the  lengths   into  which 
the   bridge-wire  is   divided.     Using  the  rheostat  resistance  as  a 
standard,  calculate,  by  means  of  the  proportion  found  in  II,  the 
resistance  of  100  cm.  of  No.  25  German  silver  wire. 

V.  Repeat  IV  with  various  coils  of  wire  on  the  table,  instead 
of  the  German  silver  wire,  and  find  the  respective  resistances  of 
these  coils.     Record  the  numbers  on  the  coils. 

VI.  Repeat  IV  with  a  coil    of  fine  copper  wire  immersed  in 
cold  water,  and  then  in  hot  water,  taking  the  temperature  of  the 
water  in   each  case  after  stirring.      From  your  "results  calculate: 
(i)  The   resistance   of  the   coil   at   each   temperature;    (2)  the 
change   in    resistance  per   degree   rise   in  temperature;  (3)  the 
resistance  at  o°;  (4)  the  change  in  resistance  per  degree  rise  in 
temperature   of  each  ohm   at   o°.     The   last  result  will  be   the 
temperature  coefficient  of  the  electrical  resistance  of  copper. 

41.     HEATING    EFFECT    OF    AN    ELECTRIC 
CURRENT. 

I.  Fill  a  small  calorimeter,  that  has  been  weighed  with  its 
stirrer,  two-thirds  full  of  icercold  water  and  weigh.  Adjust  in 
place  the  heating-coil  provided  having  the  higher  resistance,  and 
insert  a  thermometer  in  the  water  through  the  opening  in  the 
cover  to  which  the  coil  is  attached.  Stir  thoroughly,  taking 
care  not  to  splash  the  water  and  keep  stirring  throughout  the 
exercise. 


41]  HEATING    EFFECT   OF    AN    ELECTRIC    CURRENT.  75 

Connect  the  heating  coil  in  series  with  an  ammeter  and  with 
the  terminals  of  the  power  circuit  marked  ' '  large  current, 
making  the  final  connection  at  a  noted  minute  and  taking  the 
temperature  at  the  same  instant.  Read  the  temperature  and  the 
current  each  every  minute  on  alternate  half  minutes,  until  the 
temperature  is  half  as  high  above  that  of  the  room  as  it  was  below 
at  the  start. 

II.  Repeat    I    connecting   to    the    terminals    marked    "small 
current." 

III.  Repeat  I  (with  the  same  terminals  as  in  I)  using  the  coil 
of  lower  resistance. 

IV.  Calculate  the  heating  effect  of  the  current  in   each  of  the 
three  cases,  in  degrees  per  second. 

Show  from  the  results  of  I  and  II  to  what  power  of  the  current 
the  heating  is  proportional. 

From  the  results  of  I  and  III  show  how  the  heating  varies 
with  the  resistance  when  the  current  is  constant. 

V.  What  becomes  of  the  energy  expended  in  maintaining  an 
electric  current  through  a  conductor? 

Form  an  equation  representing  the  relation  of  the  heating  to 
the  current,  resistance  and  time. 

Calculate  the  heat  imparted  by  the  coil  in  I  on  the  assumption 
that  all  goes  to  the  water,  calorimeter  and  stirrer.  (The  neces- 
sary specific  heats  are  given.) 

The  energy  expended  electrically  is  given  in  joules  when  ex- 
pressed in  terms  of  the  units:  the  ampere,  ohm,  and  second. 
From  the  relation  found  above  calculate  in  joules  the  energy  ex- 
pended in  I,  using  the  average  value  of  the  current.  Deduce  the 
ratio  of  the  calorie  to  the  joule.  What  is  this  quantity? 

Calculate  in  watts  the  power  required  in  I. 

What  is  it  now  necessary  to  know  to  calculate  the  value  of  the 
watt  in  ergs  per  second?  Explain. 

VI.  By  means  of  Ohm's  Law  and  the  relation  of  V,  find  an 
expression  for  the  heating  effect  in  terms  of  the   electromotive 
force  and  the  current. 


76  LAWS   OF    ELECTROLYSIS.  [42 

42.     LAWS  OF  ELECTROLYSIS. 

1.  Scour  with  emery  cloth  the  six  plates  of  the  three  copper 
voltameters,  then  wash  and  dry  them,  taking  care  not  to  touch 
the  polished  surfaces 'and  not  lay  them  on  anything  other  than 
clean  white  paper.       Weigh  these  plates  carefully  on  a  sensitive 
Jolly  balance,  recording  the  numbers  on  the    plates  in  order  to 
identify  them  later.       Place  the  plates  in  the  dilute,  slightly  acid 
copper  sulphate  solution  which  fills  each  of  the  voltameters,  two 
plates  in  each  voltameter,  adjusting  so  that  the  plates  are  parallel 
in  each  cell.      Connect  the  voltameters  so  that  the  whole  current 
will  go  through  one  of  them  and  half  through  each  of  the  other 
two,  arranging  so  that  the  current  will  go  from  the  thick  to  the 
thin  plate  in  each  cell.      Diagram.      State  how  you  determine  the 
direction  of  the  current.      The  circuit  is  completed  by  connecting 
in  series  an  ammeter  and  storage  battery.     The  final  connection 
completing  the  circuit   is  to  be  made  at  a  noted  instant  of  time. 
Leave  the  circuit  closed  for  fifty  minutes    exactly  and  read  the 
current  every  two  minutes.      At  the  close  of  the  run  wash,  dry, 
and    weigh    the    plates    with    the    same    precautions    as    before. 
Record  on  the  diagram  the  gain  or  loss  of  each  plate. 

II.  i.   Was  the  copper  carried  with  or  against    the    current? 
Which,  then,  are    the   gain    plates,   those  by  which    the  current 
enters  or  leaves  the  cells?       How  does  the  electrolytic  cell  com- 
pare in  this  respect  with  the  voltaic  cell? 

2.  In  each  voltameter  how  did  the  gain  of  mass   in  one  plate 
compare  with  the  loss  of  mass  in  the  other? 

3.  What  relation  exists  between  the  gain  in  mass  of  the. gain 
plate  in  the  voltameter  through  which  the  whole  current  passed 
and  the  corresponding  quantities  for  the  other  two   voltameters? 
Does  the  same  relation  hold  for  the  loss  plates  ? 

Find  how  the  mass  of  copper  deposited  varies  with  the  current. 

III.  Using  the  average  value  of  the  current  in  I,  calculate  for 
each  cell  the    mass  of  copper    that  would    be  deposited,  from  a 
copper   sulphate   solution    by  a  current  of  one   ampere    in    one 


43]  ELECTROMAGNETIC    INDUCTION.  77 

second,  and  find  the  average.  This  quantity  is  known  as  the 
electro-chemical  equivalent  of  copper. 

IV.  If  zinc  electrodes  in  a  zinc  sulphate  solution  were  used, 
would  you  expect  the  same  quantity  of  zinc  to  be  deposited  in 
the  same  time  by  the  same  current,  as  above  ? 

Look  this  up  and  state  the  remaining  law  of  electrolysis. 

Express  in  the  form  of  an  equation  the  laws  of  electrolysis. 

43.     ELECTROMAGNETIC    INDUCTION. 

I.  (a.)  Connect  a  coil  of  wire  to  a  sensitive  galvanometer,  after 
testing    with    a    Leclanche    cell    what    is    the    direction    of    the 
current  corresponding  to  a  deflection  to  the  right  and  left.      (Be 
careful  not  to  disturb  the  galvanometer  and  accessory  apparatus.) 
Connect  an  electro-magnet  to  the  storage  battery  terminals. 

Hold  the  coil  in  the  field  of  the  electromagnet  perpendicular  to 
the  direction  of  the  field,  opposite  the  north  pole  of  the  magnet. 
Then  turn  the  coil  quickly  through  90°,  so  that  it  becomes 
parallel  to  the  direction  of  the  field.  Note  the  deflection  of  the 
galvanometer,  and  whether  a  clockwise  or  counter-clockwise 
current  is  induced  in  the  coil,  looking  along  the  lines  of  force. 

(^.)  With  the  coil  held  as  in  (a)  remove  the  electromagnet 
from  before  the  coil,  noting  deflection  and  direction  of  induced 
current  as  before. 

(c.*}  With  the  coil  and  magnet  as  in  (a),  break  the  circuit  of 
the  electromagnet.  Record  as  before. 

In  (d),  (£),  and  (c)  how  do  the  currents  compare  in  magnitude 
and  direction?  Viewing  the  coil  in  the  direction  of  the  lines  of 
force,  was  the  number  of  lines  through  the  coil  diminished  or 
increased  in  each  case?  Does  then  diminishing  the  number  of 
lines  of  force  through  a  closed  circuit  induce  a  clockwise  or  a 
counter-clockwise  current  in  the  circuit? 

II.  Repeat  I  (a)  with  the  same  coil  but  inserting  a  resistance 
in  the  circuit  equal  to  the  previous  total  resistance  of  the  circuit. 
Compare  the  current  induced  with  that  in  I.       How  did  it  vary 


7  8  ELECTROMAGNETIC   INDUCTION.  [43 

with  the  resistance  in  the  circuit  ?  Which  do  you  conclude  is  the 
quantity  that  remained  constant,  the  induced  current  or  the 
induced  electromotive  force?  Is  it  better  then  to  speak  of  induc- 
ing an  electromotive  force  or  a  current  by  moving  a  closed  circuit 
in  a  magnetic  field? 

III.  (#.)   Remove  the  extra  resistance,  and  rotate  the  coil  from 
its  final  position  in  I  through  another  90°.       Apply  the  rule  de- 
duced in  III,  for  the  direction  of  the    induced  current  (electro- 
motive force).     Does  it  still  hold  true? 

(£.)  Rotate  the  coil  through  180°  more  by  steps  of  90°.  What 
is  the  effect  of  increasing  the  number  of  force-lines  through  the 
coil  on  the  direction  of  the  induced  current  (electromotive  force)  ? 

(r.)  Repeat  I  (<£)  with  the  electromagnetic  turned  end  for  end. 
Is  the  result  of  III  (£)  confirmed? 

IV.  Repeat  III  (£)  with  a  coil  having  twice  as  many  turns  of 
wire.     How  do  you  find  the  induction  to  vary  with  the  number 
of  turns  of  wire  in  the  coil?     If  you  consider  each  turn  as  enclos- 
ing a  certain  number  of  force-lines,  how  then  does  the  induction 
vary  with    the    total    change    in    the    number  of  the   force-lines 
threading  through  the  coil  ? 

V.  (a.'}   Hold  the  coil  stationary,  as  in  I  (<:),  and  remove  the 
core  only  of  the  electromagnet.     If  the  galvanometer  is  deflected, 
read  the  deflection.     Replace  the  core  and  read  the  deflection,  if 
any,  again.      Explain  the  effect  in  each  case. 

(<5.)  Remove  the  core  very  slowly  and  read  the  deflection  of 
the  galvanometer.  Does  this  experiment  indicate  that  the  in- 
duced current  (electromotive  force)  varies  with  the  rate  at  which 
the  change  in  the  magnetic  field  is  produced?  How  does  the 
rate  of  change  affect  the  induced  electromotive  force  ? 

VI.  The  general    laws   of  electromagnetic    induction    may  be 
stated  thus:  When  the  magnetic  field  is  altered  in  any  way  with 
respect  to  an  electric  conductor,  an  electromotive  force  is  induced 
in  the  conductor.       This  induced  electromotive  force  is  propor- 
tional to  the  rate  of  change  in  the  magnetic  field,  and  its  direc- 


44]  EARTH    INDUCTOR.  79 

tion  is  such  as  to  produce  a  current  that  will  oppose  the  change 
in  the  field. 

Show  how  the  results  obtained  in  I-V  may  be  explained  by 
means  of  this  law. 

44.     EARTH    INDUCTOR. 

I.  (a.)  Set  up  a  sensitive  galvanometer  and  connect  it  with  an 
earth-inductor,  placing  them  as  far  apart  as  the  table  will  allow. 
Place  the  earth -inductor  so  that  the  two  stationary,  upright  sup- 
ports are  in  an  east  and  west  line,  and  set  the  circle  so  that  its 
axis- of  rotation  is  horizontal. 

Turn  the  circle  slowly  into  a  horizontal  position,  let  the 
galvanometer-needle  come  to  rest,  and  then  turn  the  circle  sud- 
denly through  1 80°,  noting  the  effect  on  the  galvanometer. 
Explain  the  cause  of  the  current  produced. 

(b. )  Turn  the  circle  in  the  same  direction  through  another 
1 80°,  and  compare  the  induced  current  with  that  in  I  («).  Was 
its  direction  the  same  ?  What  would  its  direction  have  been  if 
there  had  been  no  commutator? 

(V.)  Rotate  the  coil  continuously  and  uniformly,  recording 
the  number  of  turns  per  minute  and  the  deflection  of  the 
galvanometer. 

II.  Set  the  coil  so  that  its  axis  of  rotation  is  approximately  in 
the  direction  of  the  earth's  magnetic  field  (at  an  angle  of  about 
62°  with  the  horizontal).      Rotate  it  continuously  as  was  done  in 
I  (V),  recording  again  the  number  of  turns  per  minute  and  the 
deflection  of  the  galvanometer,  if  any.       How  does  the  current 
induced  compare  with  that   in  I  (V)?     Explain   the  difference,  if 
there  is  any. 

III.  Set  the  coil  as  in  I,  and   rotate  it  continuously  at  a  rate 
either  one-half  or  twice  as  great  as  in  I  (V).     What  effect  do  you 
find  a  change  in  the  rate  of  rotation  to  have  upon  the  value  of 
the  induced  current  ? 

IV.  Repeat  I   (c)  with  the  axis  of  rotation  vertical,  rotating 


80  EARTH    INDUCTOR.  [44 

the  coil  as  nearly  as  possible  at  the  same  rate.  To  what  com- 
ponent of  the  earth's  magnetic  field  is  the  induced  current  pro- 
portional in  this  case?  To  what  component  was  it  proportional 
in  I  (V)?  How  might  the  angle  of  dip  be  calculated  from  the 
observations  made  in  this  section  and  in  I  (V)  ?  Using  a  table  of 
natural  tangents,  calculate  thus  the  angle  of  dip  at  Berkeley. 

V.  By  varying  the  angle  of  inclination  of  the  coil,  find  a  posi- 
tion for  which  there  will  be  no  current   induced   when  the   coil   is 
rotated.      Read  the  angle  of  inclination,  if  the  earth-inductor  has 
a  graduated  circle.      What  is  the  relation  between  this  angle  and 
the  angle  of  dip?     How  does  the  value  of  the  angle  of  dip  found 
in  this  way  compare  with  that  found  in  IV? 

VI.  Turn    the    base   of  the   earth-inductor    through    90°    and 
rotate  the  coil  continuously  about  a  vertical  axis,  as  in  IV,  at  the 
same  rate.      How  do  you  find   the  induced  current    to  compare 
with  that  in  IV  ?     Explain  the  difference,  if  there  is  any. 

VII.  Answer  the  following  questions  and  give  reasons  for  your 
answers: — 

1.  Would  there  have  been  any  current  induced  if  the  coil  had 
been  moved  parallel  to  itself? 

2.  Would  there  have  been  any  current  induced  if  the  coil   had 
been    moved    parallel    to    itself    with    a   strong    magnet    in    its 
neighborhood  ? 

3.  What  would   be  the  effect  on  the   induced  current  if  a   soft 
iron  core  were  placed  within  the  coil  of  the  earth  inductor? 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 

AN  INITIAL  PINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


NOV  1*7  193Q 

ll  v»      A  »       !«7dvf 

JVJL  22  W« 

I  IRRARY  USE 

n  pv  r\            •       <lfiCO 

APR    i  1953 

. 

LD  21-100rrc-7,'39(402s) 

Y.C  91217 


10227 


RH 


^^ssasBSSB 

?M?$i%$8§® 
MSM^iSi 


w& 


, 


